ScienceWeek

SCIENCEWEEK

ScienceWeek
July 25, 2003
Vol. 7 Number 30A

An Online Digest of Research in the Sciences

---------------------------------------------

My own suspicion is that the Universe is not only queerer than we
suppose, but queerer than we can suppose.
-- J.B.S. Haldane (1892-1964)

---------------------------------------------

=-=-=-=-=-=-=-=-=

Section 1

=-=-=-=-=-=-=-=-=

Part A - Symposium: Cosmology and the Structure of the Universe

1. Introduction
2. Historical Notes
3. Geometry of the Universe
4. Structure of the Universe
5. Spacetime
6. History and Future of the Universe

Notices and Subscription Information

=-=-=-=-=-=-=-=-=

Section 2

=-=-=-=-=-=-=-=-=

1. INTRODUCTION

CONCEPTS AND TERMINOLOGY

The central problem of cosmology is to provide a self-consistent
view of the past, present, and future of the Universe that takes
into account not only concepts and observations in astrophysics
but also concepts and observations in all of physics,
particularly those in particle physics and quantum physics. Thus,
a cosmological model is a conceptual edifice built with the
bricks of fundamental physics, and as physics changes, and
observations change, so do the acceptable models. Can there be a
"final theory" in cosmology? Probably not until there is a "final
physics", a physics in which all new observations are without
surprises. We are certainly not there yet; in fact, the objective
is so distant, there is perhaps not even a glimmer of a shadow in
the murky mist. But as the astrophysicist Edwin Hubble (1889-
1953) said, "The search will continue. The urge is older than
history. It is not satisfied and it will not be oppressed."

Contemporary cosmology distinguishes two kinds of matter,
"ordinary matter" and "dark matter". In general, a baryon is a
nuclear particle (e.g., a proton) built from 3 quarks
(fundamental particles that combine to make up protons, neutrons,
and mesons), and so-called "ordinary matter" is baryonic. In this
context, the term "dark matter" refers to material whose presence
can be inferred from its effects on the motions of stars and
galaxies, but which cannot be seen directly because it emits
little or no radiation. It is believed that as much as 90 percent
of the mass in the Universe may exist as some form or dark
matter, although the proposed percentage of dark matter varies
widely with different cosmological models.

In cosmology, what is called the "Big Bang model" is at present
the most widely accepted theory of the origin and evolution of
the Universe. The essential feature of the model is the emergence
of the Universe from a state of extremely high temperature and
density that occurred approximately 15 billion years ago. Such a
model was proposed by Aleksandr Friedmann (1888-1925) in 1922,
and by Georges Lemaitre (1894-1966) in 1927, but the modern
version was developed by George Gamow (1904-1968) and others
beginning in 1946. The model essentially depends on two
assumptions: a) the general theory of relativity correctly
describes the gravitational interaction of all matter; b) the
"cosmological principle" obtains, i.e., an observer's view of the
Universe in the large depends neither on the direction of
observation nor on the location of the observer. The Big Bang
model accounts for the expansion of the Universe; the existence
of the *cosmic background radiation; and the abundance of low-
mass nuclei such as helium, helium-3, deuterium, and lithium-7,
which are predicted to have been formed approximately 1 second
after the big bang when the temperature was 10^(10) degrees
kelvin.

The inflationary model, first proposed by Alan Guth in 1980,
proposes that quantum fluctuations in the time period 10^(-35) to
10^(-32) seconds after time zero were quickly amplified into
large density variations during the "inflationary" 10^(50)
expansion of the universe in that time frame, and that these
density variations eventually led to the formation of galaxies
and clusters of galaxies.

What is known as the "cosmic microwave background radiation" was
discovered accidentally in 1964, when A.A. Penzias and R. Wilson,
measuring noise that might interfere with satellite
communications, noted a mysterious signal that was soon
interpreted to be the microwave background radiation originating
in the Big Bang. In 1978, Penzias and Wilson received the Nobel
Prize in Physics for this discovery. The cosmic microwave
background is black-body radiation (the emission radiation of a
perfect absorber of radiation) at a present temperature of 2.73
degrees Kelvin, and has an almost equal intensity in all
directions in space. The deviations from isotropic intensity,
however, are of extreme importance in theoretical cosmology.

"Redshift" (symbol: z) is a lengthening of the wavelengths of
electromagnetic radiation from a source caused either by the
movement of the source (Doppler effect) or by the expansion of
the universe (cosmological redshift). Redshift is defined as the
change in wavelength of a particular spectral line divided by the
unshifted wavelength of that line. Large redshifts imply large
radial velocities (which imply large distances, according to
current cosmological theory), but at redshifts greater than about
0.2 there is a relativistic divergence from a linear relation. A
redshift of 4.0 corresponds to an object receding with a radial
velocity 92% that of the velocity of light. The largest
astrophysical redshifts so far observed are of the order of z =
4.9. As observers of redshift, we are by definition at redshift z
= 0.

In spectroscopy, the term "fine structure" refers to the
splitting of the main spectral lines of an atom into two or more
components, each component representing a slightly different
wavelength. In general, fine structure is produced when an atom
emits light in making the transition from one energy state to
another. The split lines, which are called the "fine structure"
of the main lines, arise from the interaction of the orbital
motion of an electron with the quantum mechanical "spin" of that
electron ("spin-orbit coupling"): in essence, the spinning
electron interacts with the magnetic field produced by the
rotation of the electron about the atomic nucleus, and this
interaction generates the fine structure of the spectrum.

Given the hot Big Bang model, which proposes an intensely hot
beginning for the Universe, and the cosmic microwave background
radiation, which shows the present Universe with a background
temperature of 2.73 degrees kelvin, one can state the following:
If it is true that the Universe was intensely hot in the
beginning and has now cooled, then at some time in the past the
cosmic microwave background radiation must have had a higher
temperature than 2.73 degrees kelvin. An important question is
whether we can detect, even indirectly, such a higher-temperature
background radiation?

Central to current cosmological considerations are the
distinctions between the geometries of a "flat" (uncurved;
infinite in both extent and lifetime), "closed" (spherical;
finite in both extent and lifetime), and "open" (*hyperbolic;
infinite and expanding forever) Universe. An important quantity
is the Omega parameter, defined as the ratio of the density of
matter (or energy) in the Universe to the theoretical density
required for flatness. An Omega with a value of greater than 1
implies a closed Universe; a value less than 1 implies an open
Universe; a value equal to 1 implies a flat Universe. The problem
for the past 60 years has thus been to obtain an estimate of the
mass density of the Universe from observations. The current
standard conception is that the geometry of the Universe is flat.

ON COSMOLOGY AND THE WILKINSON PROBE

The following points are made by Sean Carroll (Nature 2003
422:26):

1) Not so long ago, cosmology was, half-jokingly, thought of as
"a search for two numbers". The numbers in question were the
Hubble constant, which measures the rate at which the Universe is
expanding, and the energy density, measured in terms of the
critical density for which the Universe is flat (that is, when
space has zero curvature). What was worse, many of the field's
own practitioners despaired of determining these numbers with any
real precision. The difficulty of controlling systematic errors
in conventional observations of objects at cosmological distances
presented a daunting obstacle.

2) In the past decade, all this has changed: our description of
the Universe is now considerably more detailed, and the most
important cosmological parameters are being determined with
precision. The change can be traced back to 1992, when NASA's
Cosmic Background Explorer (COBE) satellite first observed1 small
temperature fluctuations, or anisotropies, in the cosmic
microwave background (CMB), the relic radiation from the Big
Bang. Since then, we have obtained improved measurements of
distances to galaxies and supernovae, large-scale structure,
light-element abundances, clusters of galaxies, cosmological
dynamics and even of the CMB itself. Such measurements have
pinned down a precise picture of the state of our Universe that
was beyond the hopes of most cosmologists just a short time ago.
Now another NASA satellite, the Wilkinson Microwave Anisotropy
Probe (WMAP), has returned much higher-resolution images of CMB
fluctuations, confirming and extending this remarkable
achievement. These new results provide a worthy book-end to a
decade of startling discoveries.

3) Our Universe is expanding -- distant galaxies are moving
further away from each other. Using the laws of general
relativity and some knowledge of the Universe's constituents, we
can trace the evolution of the Universe backwards in time to an
era when the density of matter and radiation was significantly
higher and a plasma of photons, electrons and nuclei existed in
thermal equilibrium. At a temperature of approximately 3000 K
(when the Universe was about 400,000 years old), atomic hydrogen
formed and the Universe became transparent. The CMB that we
observe has (mostly) streamed freely to us from that moment,
cooling as the Universe expanded to a black-body temperature of
2.73 K.

4) Although the CMB is remarkably uniform from place to place in
the sky, small anisotropies in its temperature indicate
perturbations in density that are thought to have grown into
galaxies and large-scale structure in the contemporary Universe.
By assuming that the perturbations originated at very early
times, and have roughly equal amplitude at all length scales, we
can obtain a good fit to observations of the anisotropies as a
function of angular scale. Perturbations of different wavelengths
evolve differently as the Universe expands, but they do so in a
calculable way that depends on cosmological parameters such as
the Hubble constant and the energy density, as well as on the
amplitude of the initial fluctuation. Observations of these
anisotropies therefore reveal a great deal about the
characteristics of our Universe.

5) Perhaps the most significant aspect of the WMAP results is not
the discovery of an unexpected feature of the Universe, but the
confirmation of the generally accepted cosmological model that
has been constructed over the past several years. In this model,
the Universe is spatially flat and 14 billion years old, with an
energy density consisting of 30% matter and 70% dark energy (a
smoothly distributed component that varies slowly, if at all, as
the Universe expands). The matter comes mostly in the form of
dark matter, which is believed to be made of a type of particle
that is as yet undetected; only 4% of the total energy density of
the Universe is ordinary matter (such as stars, planets, gas and
dust). Although this model is consistent with a wide variety of
observations, it is clearly problematic from various points of
view. As ordinary matter and dark matter presumably originate
through very different mechanisms, why is their abundance so
similar (within an order of magnitude)? Worse still, why is the
total abundance of matter comparable to that of dark energy if
they are changing rapidly with respect to each other as the
Universe expands? Furthermore, the leading candidate for dark
energy is vacuum energy, or the cosmological constant, for which
theoretical estimates disagree with observations by 120 orders of
magnitude. But, as ungainly as this model appears, the WMAP
results confirm it spectacularly.

Notes:

The "Hubble constant" is a measure of the rate of expansion of
the Universe, the average value of velocity of recession divided
by distance. Since the constant is time-dependent, it is more
correctly termed a parameter. It's present value is believed to
be between 60 and 75 km/sec/megaparsec. One parsec equals 3.262
light-years, or 30.86 x 10^(12) kilometers.

COSMOLOGY: EXPECTATIONS IN THE NEXT CENTURY OF RESEARCH

The following points are made by Martin Rees (Scientific American
1999 December):

1) Astronomers still do not know what the Universe is made of.
Observable radiation-emitting objects -- such as stars, *quasars,
and galaxies -- apparently constitute only a small fraction of
the matter in the Universe. The vast bulk of matter is dark and
unaccounted for, and most cosmologists believe this dark matter
is composed of weakly interacting particles left over from the
*Big Bang. But dark matter could be something more exotic.
"Whatever the case, it is clear that galaxies, stars and planets
are a mere afterthought in a Cosmos dominated by quite different
stuff." The author suggests that intensive searches for dark
matter, mainly via sensitive underground experiments designed to
detect elusive subatomic particles, will continue in the coming
decade, and that within the next decade both the amount and
nature of dark matter will be clarified.

2) The author suggests that research in the near-future is also
likely to focus on the evolution of the large-scale structure of
the Universe. The current view is that ever since the Big Bang,
gravity has been amplifying inhomogeneities, building up
structures and enhancing temperature contrasts -- "a prerequisite
for the emergence of the complexity that lies around us now and
of which we're a part." The author suggests that astronomers are
now learning more about the 10 billion year process of Cosmic
evolution by creating virtual universes on computers, and that in
the coming years researchers will be able to simulate the history
of the Universe with ever improving realism and then compare the
results with astronomical observations.

3) The author suggests that the great mystery for cosmologists is
the series of events that occurred less than 1 millisecond after
the Big Bang, when the Universe was extraordinarily small, hot,
and dense. "The laws of physics with which we are familiar offer
little firm guidance for explaining what happened during this
critical period." To solve this problem, it will necessary to
improve and refine current observations in order to understand
the characteristics of the Universe when it was only one second
old: its expansion rate, the size of its density fluctuations,
and its proportions of ordinary atoms, dark matter, and
radiation.

4) The author suggests the following Cosmic timeline for the
evolution of the Universe from the Big Bang to the present:

a) 10^(-43) seconds after the Big Bang: the *Quantum Gravity Era.

b) 10^(-36) seconds after the Big Bang: Probable *Era of
Inflation.

c) 10^(-5) seconds after the Big Bang: Formation of protons and
neutrons from *quarks.

d) 3 minutes after the Big Bang: Synthesis of atomic nuclei.

e) 300,000 years after the Big Bang: First atoms form.

f) 1 billion years after the Big Bang: Appearance of first stars,
galaxies, and quasars.

g) 10 to 15 billion years after the Big Bang: Appearance of
modern galaxies.

5) The author concludes: "How did a hot amorphous fireball
evolve, over 10 to 15 billion years, into our complex Cosmos of
galaxies, stars, and planets? How did atoms assemble -- here on
Earth and perhaps on other worlds -- into living beings intricate
enough to ponder their own origins? These questions are a
challenge for the new millennium. Answering them may well be an
unending quest."

Notes:

quasars: (quasi-stellar objects). Extremely luminous sources
radiating energy over the entire spectrum from x-rays to radio
waves, and which are apparently the oldest and most distant
objects in the universe. They are believed to involve massive
black holes.

The Big Bang theory is the general cosmological model that
proposes that all matter and radiation in the universe originated
in an explosion at a finite time in the past.

Quantum Gravity Era: Quantum field theory is the mathematical
fusion of quantum mechanics with special relativity theory, and
the term "quantum gravity" refers to the fusion of quantum
mechanics with general relativity theory. The essential basis for
these fusions is the so-called "equivalence principle", which
identifies the mass involved in the gravitational force equation
with the inertial mass in the equation that relates any force to
the product of inertial mass and acceleration. The "quantum
gravity era" is the time-frame during which both quantum effects
and gravity determined the behavior of particles.

Era of Inflation: The inflationary model, first proposed by Alan
Guth in 1980, proposes that quantum fluctuations in the time
period 10^(-35) to 10^(-32) seconds after time zero were quickly
amplified into large density variations during the "inflationary"
10^(50) expansion of the universe in that time frame.

A "quark" is a hypothetical fundamental particle, having charges
whose magnitudes are one-third or two-thirds of the electron
charge, and from which the elementary particles may in theory be
constructed.

ScienceWeek http://www.scienceweek.com

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

2. HISTORICAL NOTES

ON 18TH AND 19TH CENTURY ASTRONOMY

The following points are made by Agnes Mary Clerke (Agnes Mary
Clerke: Popular History of Astronomy during the Nineteenth
Century. 2nd Edition. London 1893):

1) The rise of William Herschel (1738-1822) was the one
conspicuous anomaly in the astronomical history of the eighteenth
century. It proved decisive of the course of events in the
nineteenth. It was unexplained by anything that had gone before;
yet all that came after hinged upon it. It gave a new direction
to effort; it lent a fresh impulse to thought. It opened a
channel for the widespread public interest which was gathering
towards astronomical subjects to flow in.

2) Much of this interest was due to the occurrence of events
calculated to arrest the attention and excite the wonder of the
uninitiated. The predicted return of Halley's comet in 1759
verified, after an unprecedented fashion, the computations of
astronomers. It deprived such bodies forever of their portentous
character; it ranked them as denizens of the Solar System. Again,
the transits of Venus in 1761 and 1769 were the first occurrences
of the kind since the awakening of science to their consequence.
Imposing preparations, journeys to remote and hardly accessible
regions, official expeditions, international communications, all
for the purpose of observing them to the best advantage, brought
their high significance vividly to the public consciousness; a
result aided by the facile pen of Lalande, in rendering
intelligible the means by which these elaborate arrangements were
to issue in an accurate knowledge of the Sun's distance. Lastly,
Herschel's discovery of Uranus, March 13, 1781, had the
surprising effect of utter novelty. Since the human race had
become acquainted with the company of the planets, no addition
had been made to their number. The event thus broke with
immemorial traditions, and seemed to show astronomy as still
young, and full of unlooked-for possibilities.

3) Further popularity accrued to the science from the sequel of a
career so strikingly opened. Herschel's huge telescopes, his
detection by their means of two Saturnian and as many Uranian
moons, his piercing scrutiny of the sun, picturesque theory of
its constitution, and sagacious indication of the route pursued
by it through space; his discovery of stellar revolving systems,
his bold soundings of the Universe, his grandiose ideas, and the
elevated yet simple language in which they were conveyed --
formed a combination powerfully effective to those least
susceptible of new impressions.

4) This great accession of popularity gave the impulse to the
extraordinarily rapid progress of astronomy in the nineteenth
century. Official patronage combined with individual zeal
sufficed for the elder branches of science. A few well-endowed
institutions could accumulate the materials needed by a few
isolated thinkers for the construction of theories of wonderful
beauty and elaboration, yet precluded, by their abstract nature,
from winning general applause. But the new physical astronomy
depends for its prosperity upon the favor of the multitude whom
its striking results are well fitted to attract. It is, in a
special manner, the science of amateurs. It welcomes the most
unpretending cooperation. There is no one "with a true eye and a
faithful hand" but can do good work in watching the heavens. And
not infrequently prizes of discovery which the most perfect
appliances failed to grasp have fallen to the share of ignorant
or ill-provided assiduity.

5) Observers, accordingly, have multiplied; observatories have
been founded in all parts of the world; associations have been
constituted for mutual help and counsel... Modern facilities of
communication have helped to impress more deeply upon modern
astronomy its associative character. The electric telegraph gives
a certain ubiquity which is invaluable to an observer of the
skies. With the help of a wire, a battery, and a code of signals,
he sees whatever is visible from any portion of our globe,
depending, however, upon other eyes than his own, and so entering
as a unit into a widespread organization of intelligence. The
press, again, has been a potent agent of cooperation.

Related Material:

ON THE 20TH CENTURY REVOLUTION IN COSMOLOGY

The following points are made by William G. Unruh (Science 2002
295:1649):

1) In the early years of the 20th century, Ernest Rutherford
(1871-1937), the great experimental physicist at Cambridge, was
reputed to have thundered, "If anyone in my laboratory begins to
speak of the Universe, I tell him it is time to leave." Since its
beginnings, cosmology, the study of the Universe as a whole, has
been characterized by a mixture of seemingly outrageous
speculation and subsequent verification.

2) Albert Einstein (1879-1955) founded his 1915 theory of gravity
on one unexplained experimental fact -- that all objects fall in
exactly the same way in a gravitational field -- and a demand for
consistency with his theory of special relativity. Through an
unparalleled intellectual tour de force, he created a theory in
which the flow of time from place to place and the creation and
destruction of space depend on matter. Shortly thereafter,
Alexandr Friedmann (1888-1925) and Georges Lemaitre (1894-1966)
each pointed out that this theory implied that the Universe is
dynamic and had a beginning. Einstein found this conclusion
sufficiently repugnant to try to change his theory. Only a few
years later, Edwin Hubble (1889-1953) demonstrated that faint
smudges of light in the telescope were distant galaxies whose
distance from us increases faster the further they are from us,
just as had been predicted. Space really does grow, and time has
a beginning.

3) The second half of the 20th century witnessed a dazzling
increase in the ability of astronomers to make observations of
the remotest regions of the Universe. The new technologies were
manifold. Radio communications gave us radio astronomy and the
detection of the cosmic background radiation from the earliest
days of the Universe. Consumer electronics provided the charge-
coupled device camera, which enabled the imaging of galaxies
hundreds of times dimmer than the night sky itself. High
precision spectroscopy allowed the detection of the small changes
in the motion of distant stars due to planets orbiting those
stars. Cosmology has thus changed from a field dominated by
speculation and unconstrained theoretical extrapolation to an
observational science, in which theories can be abandoned because
of disagreement with observation rather than merely because of
the death of their proponents.

ScienceWeek http://www.scienceweek.com

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

3. GEOMETRY OF THE UNIVERSE

COSMOLOGY: OPEN, CLOSED, OR FLAT UNIVERSE?

The following points are made by Marc Kamionkowski (Science 1998
280:1397):

1) Determination of the geometry of the universe has been a
central goal of cosmology ever since Hubble discovered its
expansion 75 years ago.

2) The central question is whether the universe is a multi-
dimensional equivalent of a 2-dimensional surface ("flat"), a
sphere ("closed"), or a saddle ("open"). The geometry, in the
context of current theory and observations, determines whether
the universe will expand forever or eventually collapse.

3) Until now, most astronomers have pursued the geometry by
attempting to measure the mass density of the universe. According
to general relativity, if the density is equal to, larger than,
or smaller than a critical density fixed by the expansion rate,
then the universe is flat, open, or closed, respectively.

4) Another possibility is to look directly at the predicted
observational effects of a curved (open or closed) universe
versus a flat universe, and in particular at the angular power
spectrum of the cosmic microwave background. The author suggests
that in the near future a new generation of experiments will
provide substantial advances in these observations, enabling more
definitive statements about the geometry of the universe, and
that these results will in turn provide clues to the new particle
physics required to understand the inflation phase following the
Big Bang origin of the universe.

Related Material:

ON PRECISION COSMOLOGY

The following points are made by S.L. Bridle et al (Science 2003
299:1532):

1) The recent announcement by the Wilkinson Microwave Anisotropy
Probe (WMAP) satellite team of their landmark measurements of the
cosmic microwave background (CMB) anisotropy (1-3) has
convincingly confirmed important aspects of the current standard
cosmological model. The results show with high precision that
space is flat (rather than curved) and that most of the energy in
the Universe today is "dark energy", which is gravitationally
self-repulsive and accelerates the expansion of the universe. The
evidence is independent of supernovae results (4,5).

2) The measurements strongly indicate that the amplitudes of
spatial variations in density and temperature that seeded the
formation of galaxies were roughly independent of length scale,
adiabatic (all forms of energy have the same spatial variation),
and followed a Gaussian distribution -- just as predicted by the
standard Big Bang inflationary model. WMAP heralds a new age of
precision cosmology with careful error analysis, tightly
constraining many key parameters. For example, the lifetime of
the universe has been determined to be 13,400 ± 300 million
years. Furthermore, WMAP's new measurement of the CMB
polarization as a function of angular scale shows that the epoch
of cosmic re-ionization -- associated with the formation of the
first stars -- had already occurred when the Universe was several
hundred million years old.

3) At the same time we celebrate this triumph, it is important to
recognize that important issues remain. For example, it is not
yet clear whether the spectrum of temperature fluctuations is
truly consistent with inflation. The spectrum is roughly scale-
invariant, but there are hints of peculiarities, and a key
inflationary prediction -- the presence of gravitational wave
effects -- has not yet been observed. We also do not know whether
dark energy is due to an unchanging, uniform, and inert "vacuum
energy" (also known as a "cosmological constant") or a dynamic
cosmic field that changes with time and varies across space
(known as "quintessence"). "Dark matter", which is
gravitationally self-attractive, also remains mysterious: We do
not yet know its nature, nor are we certain about its density or
the amplitude of the initial ripples in its distribution.

4) Today's standard theoretical paradigm is the inflationary Big
Bang model. According to this picture, the universe began in a
state of nearly infinite temperature and density and almost
immediately entered a phase of rapid, accelerated expansion
("inflation"). This expansion smoothed out the distribution of
energy, flattened any initial warp or curvature in space, and
created tiny variations in density. To transform these density
variations into the gravitationally collapsed, complex structures
we see today, it is essential that there be "dark matter" as well
as ordinary (baryonic) matter. Finally, we need dark energy to
account for the measured total energy density and to explain the
current cosmic acceleration.

References (abridged):

1. C. Bennett et al., in preparation (
http://arXiv.org/abs/astro-ph/0302207 ).

2. G. Hinshaw et. al., in preparation (
http://arXiv.org/abs/astro-ph/0302217 ).

3. A. Kogut et. al., in preparation ( http://arXiv.org/abs/astro-
ph/0302213 ).

4. S. Perlmutter et al., Astrophys. J. 517, 565 (1999)

5. A. G. Riess et al., Astron. J. 116, 1009 (1998)

Notes:

WMAP is a NASA Explorer Mission to measure the temperature of the
cosmic background radiation

Related Material:

ON DIMENSIONS AND GEOMETRIES

The following points are made by Lisa Randall (Science 2002
296:1422):

1) We generally take it for granted that we live in a world where
there are three infinite spatial dimensions. In fact, we rarely
give this fact much thought; we readily refer to left-right,
forward-backward, and up-down.

2) Yet the most exciting developments in particle physics in the
past few years have involved the recognition that additional
dimensions might exist and furthermore might play a role in
determining our observable world. New theoretical discoveries are
evolving at a very rapid rate. The potential implications range
from experimental signatures of extra dimensions, to
understanding fundamental questions about the nature of gravity,
to new insights into the evolution of our universe.

3) One of the chief motivations for considering additional
dimensions came from string theory, which in turn is motivated by
the failure of classical gravity to work at very short distance
scales or, equivalently, at very high energies, where quantum
mechanical effects cannot be neglected. The only known way to
consistently reconcile quantum mechanics with Einstein's theory
of gravity is string theory, in which the fundamental objects
that constitute our universe are not particles but (very tiny)
extended objects: "strings". It appears that one can only have a
consistent string theory that can describe the known particles if
there are many additional spatial dimensions: six or seven,
depending on how one looks at it. The question is, then, why
don't we see these additional directions? What has become of
them? Can they play any role in the physics we see? And is there
any chance we will observe them soon?

4) There are two known ways to incorporate additional dimensions
of space that are consistent with what we see, or rather what we
don't see; namely Kaluza's (1,2) original idea of curling them up
into little balls (compactification) or the more recent proposal
by Sundrum and Randall of focusing of the gravitational potential
in a lower dimensional subspace (localization) (3,4). These ideas
are important in and of themselves; one or the other would be the
reason we so far haven't observed evidence for extra dimensions,
should they exist. Another exciting development in the field of
extra dimensions is the fact that even though the dimensions have
not yet been seen directly, their existence might explain
important features of the observed standard model and will be
observed in the near future should these conjectures prove
correct.

5) In summary: The field of extra dimensions, as well as the
hypothesized sizes of extra dimensions, have grown by leaps and
bounds over the past few years. The reasons for the recent
activity in this field include the observations that extra
dimensions can be macroscopic or even infinite in size. Another
new development is the application of extra dimensions to the
determination of particle physics parameters and properties.

References (abridged):

1. T. Kaluza, Preuss. Akad. Wiss. 966 (1921)

2. O. Klein, Z. Phys. 37, 895 (1926)

3. L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999)

4. L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999)

Related Material:

CMB RADIATION AND EVIDENCE FOR A FLAT UNIVERSE

The following points are made by P. De Bernardis (Nature 2000
404:955):

1) The blackbody radiation left over from the Big Bang has been
transformed by the expansion of the Universe into the nearly
isotropic 2.73 K cosmic microwave background. Tiny
inhomogeneities in the early Universe left their imprint on the
microwave background in the form of small anisotropies in its
temperature. These anisotropies contain information about basic
cosmological parameters, particularly the total energy density
and curvature of the Universe.

2) Photons in the early Universe were tightly coupled to ionized
matter through Thomson scattering. This coupling ceased about
300,000 years after the Big Bang, when the Universe cooled
sufficiently to form neutral hydrogen. Since then, the primordial
photons have traveled freely through the Universe, redshifting to
microwave frequencies as the Universe expanded. We observe those
photons today as the cosmic microwave background (CMB). An image
of the early Universe remains imprinted in the temperature
anisotropy of the CMB. Anisotropies on angular scales larger than
2° are dominated by the gravitational redshift the photons
undergo as they leave the density fluctuations present at
decoupling(1,2). Anisotropies on smaller angular scales are
enhanced by oscillations of the photon–baryon fluid before
decoupling(3). These oscillations are driven by the primordial
density fluctuations, and their nature depends on the matter
content of the Universe.

3) The authors report the first images of resolved structure in
the microwave background anisotropies over a significant part of
the sky. Maps at four frequencies clearly distinguish the
microwave background from foreground emission. The authors
compute the angular power spectrum of the microwave background,
and report their results are consistent with that expected for
cold dark matter models in a flat (Euclidean) Universe, as
favored by standard inflationary models.(4,5)

References (abridged):

1. Sachs,R. K. & Wolfe,A. M. Perturbations of a cosmological
model and angular variations of the microwave background.
Astrophys. J. 147, 73-90 (1967)

2. Weinberg, S., Gravitation and Cosmology (Wiley & Sons, New
York, 1972)

3. Hu,W., Sugiyama,N. & Silk,J. The physics of cosmic microwave
background anisotropies. Nature 386, 37-43 (1997)

4. Bond,J. R., Efstathiou,G. & Tegmark,M. Forecasting cosmic
parameter errors from microwave background anisotropy
experiments. Mon Not. R. Astron. Soc. 291, L33-L41 (1997)

5. Hinshaw,G. et al. Band power spectra in the COBE-DMR four-year
anisotropy map. Astrophys. J. 464, L17-L20 (1996)

Related Material:

ON THE COSMIC TRIANGLE

The following points are made by N.A. Bahcall et al (Science 1999
284:1481):

1) Novel technologies are opening new windows on the Universe.
Whereas previously we relied primarily on fossil evidence found
in the local neighborhood of our Galaxy to infer the history of
the Universe, now we can directly see the evolution of the
Universe over the past 15 billion years, extending as far back as
a few 100,000 years after the Big Bang. Thus far, the picture of
the past history of the cosmos has altered only slightly; the
observations are consistent with the standard Big Bang model of
the expansion of the Universe from a hot dense gas, the synthesis
of the elements in the first few minutes, and the growth of
structure through the gravitational amplification of small
initial inhomogeneities.

2) However, the expectation for the future has been dramatically
revised. On the basis of the conventional assumption that the
Universe contains only matter and radiation -- the forms of
energy we can readily detect -- the expectation for the future
had been that the expansion rate of the Universe would slow
continuously because of the gravitational self-attraction of
matter. The major issue seemed to be whether the Universe would
expand forever or ultimately recollapse to a big crunch. Now, the
evidence is forcing us to consider the possibility that some
cosmic dark energy exists that opposes the self-attraction of
matter and causes the expansion of the universe to accelerate.

3) Since the discovery of cosmic expansion by Hubble (1) in the
1920s, the standard assumption had been that all energy in the
universe is in the form of radiation and ordinary matter
(electrons, protons, neutrons, and neutrinos, with mass counting
as energy at the rate E = mc^(2)). Over the next several decades,
though, theory concerning the stability of galaxies (2),
observations of the motion of galaxies in clusters (3,4), and
observations of the motion of stars and gas surrounding galaxies
(5) indicated that most of the mass in the universe is dark and
does not emit or absorb light. In the 1980s, the proposal of dark
matter found resonance in the inflationary universe scenario, a
theory of the first 10-30 seconds designed to address several
questions left unanswered by the Big Bang model: Why is the
universe so homogeneous and isotropic? Why is the curvature of
space so insignificant? And, where did the initial
inhomogeneities that give rise to the formation of structure come
from?

4) In summary: The author introduces the "cosmic triangle" as a
way of representing the past, present, and future status of the
universe. Our current location within the cosmic triangle is
determined by the answers to three questions: How much matter is
in the universe? Is the expansion rate slowing down or speeding
up? And, is the universe flat? A review of recent observations
suggests a universe that is lightweight (matter density about
one-third the critical value), is accelerating, and is flat. The
acceleration implies the existence of cosmic dark energy that
overcomes the gravitational self-attraction of matter and causes
the expansion to speed up.

References (abridged):

1. E. Hubble, Proc. Natl. Acad. Sci. U.S.A. 15, 168 (1929)

2. J. P. Ostriker and P. J. E. Peebles, Astrophys. J. 186, 467
(1973)

3. F. Zwicky, Helv. Phys. Acta 6, 110 (1933) ; S. Smith,
Astrophys. J. 83, 23 (1936)

4. N. A. Bahcall, Annu. Rev. Astron. Astrophys. 15, 505 (1977)

5. H. W. Babcock, Lick Obs. Bull. 19, 41 (1939) ; M.
Schwarzschild, Astron. J. 59, 273 (1954)

Related Material:

ON THE CMB AND THE GEOMETRY OF THE UNIVERSE

The following points are made by Craig J. Hogan (Nature 2000
408:47):

1) Recent measurements of temperature variation in the cosmic
microwave background reveal distinctive patterns in these
fluctuations, patterns which depend on the details and
composition of the Universe, and cosmologists are beginning to
interpret these patterns through detailed statistical studies.
The results are in accord with the expectations of inflation --a
nearly "flat" Universe, which can be described as a small piece
of an enormous *hypersphere -- and in accord with independent
estimates of various quantities such as the density of dark
matter.

2) Nevertheless, there are several unexpected and possibly
important discrepancies. The sharpest and most interesting
discrepancy is the estimate of the density of ordinary (baryonic)
matter in the Universe: the new data suggest that the mean number
of neutrons and protons per unit volume is greater than was
thought.

3) The author concludes: "Exploration of this discrepancy might
lead to something really new -- perhaps a simple reinterpretation
of data on abundances, or perhaps a new ingredient not yet
included in the standard cosmological model."

Notes:

If one considers a circle (2-dimensional), a sphere (3-
dimensional), the term "hypersphere" refers to the subsequent
members of the series, where the number of dimensions is >= 4. A
hypersphere is thus defined as the set of n-tuples of points
[x(sub1), x(sub2), ..., x(subn)] such that x(sub1)^(2) +
x(sub2)^(2) + ... + x(subn)^(2) = R^(2) where R is the radius of
the hypersphere.

AGE ESTIMATES OF GLOBULAR CLUSTERS IN THE MILKY WAY: CONSTRAINTS
ON COSMOLOGY

The following points are made by L.M. Krauss and Brian Chaboyer
(Science 2003 299:65):

1) Hubble's first measurement of the expansion of the Universe in
1929 also resulted in an embarrassing contradiction: Working
backward, on the basis of the expansion rate he measured, and
assuming that the expansion has been decelerating since the Big
Bang -- as one would expect given the attractive nature of
gravity -- allowed one to put an upper limit on the age of the
Universe since the Big Bang of 1.5 billion years ago (Ga). Even
in 1929 this age was grossly inconsistent with well-accepted
lower limits on the age of Earth. Although this contradiction
evaporated as further measurements of the expansion rate of the
Universe yielded a value that was up to an order of magnitude
less than Hubble's estimate, much of the subsequent history of
20th-century cosmology has involved a continued tension between
the so-called Hubble age -- derived on the basis of the Hubble
expansion -- and the age of individual objects within our own
galaxy.

2) Of special interest in this regard are perhaps the oldest
objects in our galaxy, called globular clusters. Compact groups
of 100,000 to 1 million stars with dynamical collapse times of
less than 1 million years, many of these objects are thought to
have coalesced out of the primordial gas cloud that only later
collapsed, dissipating its energy and settling into the disk of
our Milky Way Galaxy. Those globular clusters that still populate
the halo of our galaxy are thus among the oldest visible objects
within it, a fact confirmed by measuring the abundance of heavy
elements such as iron in stars within such clusters. This
abundance can be less than one-hundredth of that measured in the
Sun, which suggests that the gas from which these objects
coalesced had not previously experienced significant star
formation and evolution. Thus, an accurate determination of the
age of the oldest clusters can yield one of the most stringent
lower limits on the age of our galaxy, and thus the Universe.

3) Globular cluster age estimates in the 1980s fell in the range
of 16 to 20 Ga (1-3), producing a new apparent incompatibility
with the Hubble age, then estimated to be 10 to 15 Ga on the
basis of an estimated lower limit on the Hubble constant H(sub0)
of 50 to 75 km/sec/Megaparsec. This provided one of the earliest
motivations for reintroducing a cosmological constant into
astrophysics. Such a term in Einstein's equations results in an
increased Hubble age because it allows for a cosmic acceleration,
implying a slower expansion rate at earlier times. Thus, galaxies
located a certain distance away from us today would have taken
longer to achieve this separation since the Big Bang than they
otherwise would have. However, as more careful examinations of
uncertainties associated with stellar evolution were performed,
as well as refined estimates of the parameters that govern
stellar evolution, the lower limit on globular cluster ages
progressively decreased, so that a wide range of cosmological
models produced Hubble ages consistent with this lower limit
(4,5).

4) In summary: Recent observations of stellar globular clusters
in the Milky Way Galaxy, combined with revised ranges of
parameters in stellar evolution codes and new estimates of the
earliest epoch of globular cluster formation, result in a 95%
confidence level lower limit on the age of the Universe of 11.2
billion years. This age is inconsistent with the expansion age
for a flat Universe for the currently allowed range of the Hubble
constant, unless the cosmic equation of state is dominated by a
component that violates the strong energy condition. This means
that the three fundamental observables in cosmology -- the age of
the Universe, the distance-redshift relation, and the geometry of
the Universe -- now independently support the case for a dark
energy-dominated Universe.

References (abridged):

1. K. Janes and P. Demarque, Astrophys. J. 264, 206 (1983)

2. G. G. Fahlman, H. B. Richer, D. A. Vandenberg, Astrophys. J.
Suppl. Ser. 58, 225 (1985)

3. A. Chieffi and O. Straniero, Astrophys. J. Suppl. Ser. 71, 47
(1989)

4. B. Chaboyer, P. Demarque, P. Kernan, L. M. Krauss, Science
271, 957 (1996)

5. B. Chaboyer, P. Demarque, P. Kernan, L. M. Krauss, Astrophys.
J. 494, 96 (1998)

ScienceWeek http://www.scienceweek.com

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

4. STRUCTURE OF THE UNIVERSE

ON COSMOLOGICAL THEORIES

The following points are made by James Peebles (Scientific
American 2001 January):

1) Peebles suggests that cosmologists have firmly established the
foundations of their field, gathering over the past 70 years
abundant evidence that the Universe is expanding and cooling:

a) The light from distant galaxies is shifted toward the red, as
it should be if space is expanding and galaxies are pulled away
from one another.

b) A sea of thermal radiation fills space, as it should if space
was previously denser and hotter.

c) The Universe contains large amounts of deuterium and helium,
as it should if temperatures were once much higher.

d) Galaxies billions of years ago look distinctly younger, as
they should if they are close to the time when no galaxies
existed.

e) The curvature of space-time seems to be related to the
material content of the Universe, as it should be if the Universe
is expanding according to the predictions of Einstein's gravity
theory -- the general theory of relativity.

The author points out that the idea that the Universe is
expanding and cooling is the essence of the Big Bang theory, and
the author states: "You will notice I have said nothing about an
'explosion' -- the Big Bang theory describes how our Universe is
evolving, not how it began."

2) Peebles points out that we do not know what the Universe was
doing before it was expanding. A leading theory, "*inflation", is
an attractive addition to the framework of cosmology, but it
lacks support from various other parts of the framework, and such
support is precisely what cosmologists are now seeking. If
measurements in progress agree with the unique signatures of
inflation, then such measurements will be counted as a persuasive
argument for inflation theory. "But until that time, I would not
settle any bets on whether inflation really happened. I am not
criticizing the theory; I simply mean that this is brave,
pioneering work still to be tested."

3) Concerning the current use of the "*cosmological constant" as
an explanatory concept in understanding the evidence for an
accelerating Universe, Peebles states: "The evidence is
impressive, but I am still uneasy about details of the case for
the cosmological constant, including possible contradictions with
the evolution of galaxies and their spatial distribution. The
theory of the accelerating Universe is a work in progress. I
admire the architecture, but I would not want to move in just
yet."

4) Peebles concludes: "Over time, inflation, *quintessence, and
other concepts now under debate either will be solidly integrated
into the central framework or will be abandoned and replaced by
something better. In a sense, we are working ourselves out of a
job. But the Universe is a complicated place, to put it mildly,
and it is silly to think we will run out of productive lines of
research anytime soon. Confusion is a sign that we are doing
something right: it is the fertile commotion of a construction
site."

Notes:

The inflationary model, first proposed by Alan Guth in 1980,
proposes that quantum fluctuations in the time period 10^(-35) to
10^(-32) seconds after time zero were quickly amplified into
large density variations during the "inflationary" 10^(50)
expansion of the universe in that time frame.

In cosmology, the "cosmological constant" is a mathematical term
introduced by Einstein into the equations of general relativity,
the purpose to obtain a solution of the equations corresponding
to a "static universe". The term describes a pressure (if
positive) or a tension (if negative) which can cause the Universe
to expand or contract even in the absence of any matter. In other
words, the cosmological constant represents an effective "vacuum
energy". When the expansion of the Universe was discovered,
Einstein apparently began to regard the introduction of this term
as a mistake, and he described the cosmological constant as the
"greatest mistake of my life". But the term has reappeared as the
proposed source of apparent accelerated cosmic expansion.

Related Background:

ON QUINTESSENCE AND THE EVOLUTION OF THE COSMOLOGICAL CONSTANT

The following points are made by James Peebles (Nature 1999
398:25):

1) Contrary to expectations, the evidence is that the Universe is
expanding at approximately twice the velocity required to
overcome the gravitational pull of all the matter the Universe
contains. The implication of this is that in the past the greater
density of mass in the Universe gravitationally slowed the
expansion, while in the future the expansion rate will be close
to constant or perhaps increasing under the influence of a new
type of matter that some call "quintessence".

2) Quintessence began as Einstein's cosmological constant,
Lambda. It has negative gravitational mass: its gravity pushes
things apart.

3) Particle physicists later adopted Einstein's Lambda as a good
model for the gravitational effect of the *active vacuum of
quantum physics, although the idea is at odds with the small
value of Lambda indicated by cosmology.

4) Theoretical cosmologists have noted that as the Universe
expands and cools, Lambda tends to decrease. As the Universe
cools, *symmetries among forces are broken, particles acquire
masses, and these processes tend to release an analogue of
*latent heat. The vacuum energy density accordingly decreases,
and with it the value of Lambda. Perhaps an enormous Lambda drove
an early rapid expansion that smoothed the primeval chaos to make
the near uniform Universe we see today, with a decrease in Lambda
over time to its current value. This is the cosmological
inflation concept.

5) The author suggests that the recent great advances in
detectors, telescopes, and observatories on the ground and in
space have given us a rough picture of what happened as our
Universe evolved from a dense, hot, and perhaps quite simple
early state to its present complexity. Observations in progress
are filling in the details, and that in turn is driving intense
debate on how the behavior of our Universe can be understood
within fundamental physics.

Notes:

active vacuum of quantum physics: This refers to the idea that
the vacuum state in quantum mechanics has a zero-point energy
(minimum energy) which gives rise to vacuum fluctuations, so the
vacuum state does not mean a state of nothing, but is instead an
active state.

symmetries among forces are broken: If a theory or process does
not change when certain operations are performed on it, the
theory or process is said to possess a symmetry with respect to
those operations. For example, a circle remains unchanged under
rotation or reflection, and a circle therefore has rotational and
reflection symmetry. The term "symmetry breaking" refers to the
deviation from exact symmetry exhibited by many physical systems,
and in general, symmetry breaking encompasses both "explicit"
symmetry breaking and "spontaneous" symmetry breaking. Explicit
symmetry breaking is a phenomenon in which a system is not quite,
but almost, the same for two configurations related by exact
symmetry. Spontaneous symmetry breaking refers to a situation in
which the solution of a set of physical equations fails to
exhibit a symmetry possessed by the equations themselves.

latent heat: In general, this is the quantity of heat absorbed or
released when a substance changes its physical phase (e.g., solid
to liquid) at constant temperature.

ON THE MASS OF THE UNIVERSE

Although galaxies are arranged into gravitationally bound
clusters and superclusters, it is the galaxies themselves that
are usually considered to be the fundamental macroscopic units of
the Universe. One reason is historical, since until recently no
structures larger than a galaxy could be studied. Another reason
is the huge contrast in visible brightness between galaxies and
their surroundings. However, when one uses instruments sensing
the x-ray part of the spectrum rather than the optical light part
of the spectrum, clusters of galaxies are the most impressive
individual structures. Perhaps a good analogy concerning the
distribution of galaxies is to consider a flask containing a
rather dense culture of bacteria in a liquid medium. With the
naked eye, at zero magnification, the density distribution of
bacteria may appear uniform; with moderate magnification,
clustering, filaments, walls, voids in the culture are evident,
each cluster or filament containing millions of bacteria; at high
magnification, with a few dozen bacteria in the field, there is
again a uniformity in distribution, the larger-scale
nonuniformity not apparent.

The most striking aspect of galaxies is their apparent recession.
The term "redshift" (symbol: z) is a lengthening of the
wavelengths of electromagnetic radiation from a source caused
either by the movement of the source away from the observer
(Doppler effect; Doppler redshift) or by the expansion of the
Universe (cosmological redshift). Redshift is defined as the
increase in wavelength of a particular spectral line divided by
the unshifted wavelength of that line. Large redshifts imply
large radial velocities (which imply large distances, according
to current cosmological theory), but at redshifts greater than
about 0.2 there is a relativistic divergence from a linear
relation. A redshift of 4.0 corresponds to an object receding
with a radial velocity 92% that of the velocity of light.

A Doppler spectral change can be either a shift to the red
(redshift) or a shift to the blue (blueshift) part of the
spectrum: movement of the source toward the observer produces a
blueshift [*Note #1]. Except for local galactic movements, no
cosmological blueshifts are known, and this emphasizes the
difference between Doppler redshift and cosmological redshift:
Usually, when we speak of a Doppler redshift implying a certain
recessional velocity, we mean that the shift is due to the
inherent motion of the source relative to the observer. But
regarding cosmological (galactic) redshifts in such a manner
leads to a picture of all galaxies streaming away from us, such a
picture implicitly placing our Galaxy in the center of some great
explosion, a point of view inconsistent with the "cosmological
principle", which holds that there is no center to the Universe,
that the Universe is everywhere isotropic on the largest scales
(from which it follows that the Universe is also homogeneous).
Thus, the apparent recession velocity of galaxies is something
different from the usual concept of a recession velocity, and in
fact cosmological redshift is due to the properties of space
itself, and since the shift is to the red end of the spectrum,
the implication is that space is expanding everywhere, with every
galaxy seeing every other galaxy receding. This overall motion of
galaxies away from one another is called the "Hubble flow" after
its discoverer Edwin Hubble (1889-1953).

One of the central questions of cosmology is whether this
expansion will continue indefinitely, or whether it will
ultimately be slowed down by the intrinsic gravitational force
that tends to pull the mass of the Universe together. In any
theoretical approach to this question, a critical parameter is
the actual mass density (or more specifically, mass-energy
density) of the Universe. The term "critical density" refers to
the mass-energy density that theoretically stops the expansion of
space after infinite cosmic time has elapsed.

Also central to current cosmological considerations are the
distinctions between the geometries of a "flat" (uncurved;
infinite in both extent and lifetime), "closed" (spherical;
finite in both extent and lifetime), and "open" (*hyperbolic;
infinite and expanding forever) Universe. The term "Omega
parameter" (density parameter) is defined as the ratio of the
actual mass-energy density to the critical density required for
flatness. An Omega with a value of greater than 1 implies a
closed Universe; a value less than 1 implies an open Universe; a
value equal to 1 implies a flat Universe. The problem for the
past 60 years has thus been to obtain an estimate of the mass
density of the Universe from observations.

In this context, the intrinsic motion of a galaxy due to its
particular responses to forces such as local gravitational
attractions is called the "peculiar motion" of the galaxy, and
its velocity due to such movement is called its "peculiar
velocity". The adjective "peculiar" does not imply that the
velocity is due to anything strange, but refers simply to local
ordinary classical Doppler shifts due to the unique motions of a
given galaxy, as distinct from the overall Hubble flow. The net
redshift of a galaxy is a superposition of the peculiar Doppler
shift upon any cosmological redshift.

The following points are made by J.A. Peacock et al (Nature 2001
410:169):

1) The authors point out that Hubble demonstrated in 1934 that
the pattern of galaxies on the sky is non-random, and since that
time there have been ambitious attempts to map the distribution
of visible matter on cosmological scales. In order to obtain a 3-
dimensional picture, redshift surveys use Hubble's law, which
states that recession velocity is directly proportional to
distance from the observer, to infer approximate radial distances
to a set of galaxies. The first major surveys of this sort
occurred in the early 1980s and were limited to a few thousand
redshifts. In the 1990s, redshift surveys were extended to much
larger volumes, and these studies established that the Universe
was close to uniform in galaxy distribution on large scales, but
with a complex nonlinear supercluster network of walls,
filaments, and voids on middle scales.

2) The authors point out that the origin of middle-scale
cosmological structure is one of the key issues in cosmology. A
plausible assumption is that structure grows by gravitational
collapse of density fluctuations that are small at early times.
One important signature of gravitational instability is that
collapsing structure should generate "peculiar velocities" that
distort the uniform Hubble expansion. In general, forming
superclusters of galaxies should generate a systematic infall of
other galaxies, and this would be evident in the pattern of
recessional velocities, the effect causing an anisotropy in the
inferred spatial clustering of galaxies.

3) The authors report a precise measurement of this clustering of
galaxies, using the redshifts of more than 141,000 galaxies from
the "Two-Degree-Field" (2dF) Galaxy Redshift Survey that began in
1998 and which should be finished at the end of 2001. The authors
report their results favor a low-density Universe with Omega =
0.3.

In a commentary on this work, the following points are made by
Marc Davis (Nature 8 Mar 01 410:153):

1) The author (Davis) points out that the results of Peacock et
al suggest that the amount of mass associated with galaxy
clustering is approximately 30 percent of the cosmic critical
density, the value at which the mass of the Universe, by the
backward pull of gravity, is just sufficient to eventually stop
the Hubble expansion. This estimated density is consistent with
the result of other methods, suggesting that cosmologists are
finally converging on a reliable estimate of the mean mass
density of the Universe. All indications point to an infinite
Universe that will expand forever.

2) The author (Davis) concludes: "As additional pieces of the
puzzle fall into place, our picture of Big Bang cosmology has
become ever more bizarre. A unifying principle is clearly needed
to explain the many disparate components of the Universe we have
so far discovered. The quest for such unification is likely to
keep us busy for decades to come."

Notes:

Note #1: Our own Galaxy and the nearby Andromeda galaxy are in
gravitational association, and the Andromeda Doppler shift is in
fact blue, since the Andromeda galaxy is moving toward us.

hyperbolic: This is a negative curvature, like the surface of a
saddle, and it is sometimes called a "saddle" Universe. In such a
geometry, the sum of the angles of a triangle is less than 180
degrees. In a spherical (closed) geometry, the sum of angles is
more than 180 degrees; in a flat geometry, the sum of angles is
exactly 180 degrees.

Related Material:

LARGE-SCALE STRUCTURES IN THE UNIVERSE

As currently defined, the field of "cosmology" is the study of
the entire observable Universe treated as a single entity. Three
recognized central questions in this field are a) What did the
Universe look like at the dawn of time? b) How did it grow and
develop into what we live in today? c) What forms of matter, both
ordinary and exotic, does the Universe contain? Related to all
three of these questions are relatively recent observations
concerning the large-scale structure of the Universe,
particularly the structure of the distribution of the galaxies.
Each galaxy consists of a relatively local assemblage of hundreds
of millions or billions of stars, with enormous distances between
the galaxies. A cube set down at random in the Universe would
need to have sides 10 million light years long to contain, on
average, one galaxy. Apparently, however, the galaxies are not
distributed randomly in space: most are in groups or clusters,
pulled together by gravity. Some clusters contain many hundreds
of galaxies, and the clusters and groups are themselves arranged
in still larger filamentary or sheetlike structures. The
existence of such large-scale structures is a serious constraint
on cosmological models, and difficult to reconcile with the
"Cosmological Principle", which is the idea that the Universe
overall is homogeneous and isotropic.

The following points are made by Stephen D. Landy (Scientific
American 1999 June):

1) On all scales observed thus far by astronomers, galaxies
appear to cluster and form intricate structures -- presumably
through physical processes that were dominant during the early
expansion of the Universe and later through gravitational
interactions.

2) Over the past several years, technological advances have
enabled astronomers and cosmologists to probe the arrangement of
galaxies at great distances, and the naive notion that at some
scale the Cosmos becomes uniform has been replaced by an
appreciation that the large-scale structure of the Universe must
be understood in terms of random processes: the homogeneity and
isotropicity of the Universe is true only in a subtle statistical
sense.

3) As one moves from our own Galaxy to the entire observable
Universe, clumpiness finally gives way to smoothness. A galaxy is
a lump of stars, gas, dust, and unclassified "*dark matter". It
agglomerates with other galaxies to form galaxy clusters, the
largest bodies in the Universe held together by gravity. The
clusters, in turn, are clumped together into superclusters and
*walls, separated by voids of nearly empty intergalactic space.
Up to some scale, thought to be approximately 100 million light-
years, these progressively larger structures form a *fractal
pattern, i.e., they are equivalently clumpy on every scale. But
between this scale and the size of the observable Universe, the
clumpiness gives way to near uniformity.

4) So-called "cold dark matter models" are now the most popular
explanation for the growth of structure in the distribution of
galaxies. The premise of these models is that most of the mass in
the Universe resides in some unseen ("dark") and relatively
massive type of particle. The particle is "cold" because it is
massive and travels slowly. The particle interacts with ordinary
matter only via the force of gravity, and could also account for
the apparent *missing mass in galaxies and galaxy clusters. The
observed "*power spectrum" of the distribution of galaxies in the
Cosmos generally follows the predictions of the cold dark matter
models. But the power increases dramatically on scales of 600
million to 900 million light years, and this discrepancy
indicates that the Universe is much clumpier on those scales than
current theories can explain.

Notes:

In this context, the term "walls" refers to structured
distributions of galaxies, e.g., a clustering 750 million light-
years long, 250 million light-years wide, and 20 million light-
years thick.

A fractal is a geometrical shape whose structure is such that
magnification by a given factor reproduces the original object.
During the past several decades, the idea that fractal geometry
is an appropriate geometry to describe nature has been proposed
by many researchers. The mathematical constructs involved are
appealing because of their symmetries, and as in the development
of many appealing ideas, the use of the term "fractal" has
increased to the point where experimental observations in all the
sciences are being analyzed and interpreted as examples of
systems with apparently fractal properties. To the mathematician,
however, the definition of the property of "fractality" involves
a quantitative requirement of infinitely many orders of magnitude
of power-law scaling of the parameters of the system -- certainly
at least a spanning of many orders of magnitude.

In galaxies, particularly in spiral galaxies, the "missing mass
problem" concerns our inability to account for the motions of
stars at the edges of the galaxy using estimates of galactic mass
based on luminosities of the galaxy members. At the level of
clusters of galaxies, the missing mass problem is more a question
of assumptions concerning the physical basis of nonuniform
distributions of galaxies. In both cases, it is a matter of
asking what one would need to postulate in order to explain
observational data.

In this context, the term "power spectrum" is synonymous with
frequency spectrum, but the term "frequency" refers not to a
distribution of events in time, but rather to a distribution of
points (galaxies) in space. Essentially, the same mathematics
used to analyze event frequencies can be used to analyze
distribution frequencies. The power spectrum considered here is a
Fourier transform of the autocorrelation function familiar in
event frequency analysis (e.g., analysis of neuron outputs), but
in this case applied to spatial distribution frequencies. The
essential idea is that given a distribution of a large number of
points in space, one can apply well-known analytic techniques to
determine the degrees of local and global randomness of the
distribution. Thus, in this context, galaxies are treated as
points. One of the graphics in the Landy paper is a map of the
distribution of 3 million galaxies, each galaxy a point which
contains billions of stars.

Related Material:

COSMOLOGY: THE END OF THE OLD MODEL UNIVERSE

The following points are made by Peter Coles (Nature 1998
393:741):

1) Observations only recently made possible by improvements in
astronomical instrumentation have put theoretical models of the
Universe under intense pressure. The standard ideas of the 1980s
about the shape and history of the Universe have now been
abandoned -- and cosmologists are now taking seriously the
possibility that the Universe is pervaded by some sort of "vacuum
energy" whose origin is not at all understood.

2) The weakness of the Big Bang model is that the numerical
values of certain essential parameters in the model (the Hubble
constant, the density parameter, and, in some versions, the
cosmological constant) are not predicted by theory, and thus the
parameters must be inferred from observations.

3) The Big Bang model does not deserve to be called a "theory"
unless and until it can explain how nonuniformities of galaxies
and clusters of galaxies came into being and evolved.

4) The Cold Dark Matter model of structure formation, first
proposed in the 1980s, is in serious difficulty because the
consequent significant gravitational brake on expansion is not
evident, and in fact expansion may be accelerating. Current
observations coupled with current dynamical arguments all suggest
a global density of matter in the Universe less than the value
required to make the Universe recollapse.

5) The existence of a cosmological constant (or vacuum energy) of
the required size necessary to make the basic cosmological models
work is not at all explained by current theories of the
fundamental interactions of matter.

6) There is every reason to be confident that the important
issues will soon be resolved, because a data explosion is about
to engulf cosmology, a new generation of galaxy surveys. The
Sloan Digital Sky Survey, for example, will encompass more than a
million galaxies. The cosmological community is bracing itself
for the arrival of these enormous new data sets and the new
insights they will surely bring.

7) It is possible that none of the available models will fit all
the new data. Coles concludes: "For many of us, that is the most
exciting possibility of all, as we would have to move to stranger
theories, perhaps not even based on General Relativity."

ScienceWeek http://www.scienceweek.com

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

5. SPACETIME

ON SPACETIME

The following points are made by Max Tegmark (Science 2002
296:1427):

1) Traditionally, space was merely a three-dimensional (3D)
static stage where the cosmic drama played out over time.
Einstein's theory of general relativity (1) replaced this concept
with 4D spacetime, a dynamic geometric entity with a life of its
own, capable of expanding, fluctuating, and even curving into
black holes. Now, the focus of research is increasingly shifting
from the cosmic actors to the stage itself. Triggered by progress
in detector, space, and computer technology, an avalanche of
astronomical data is revolutionizing our ability to measure the
spacetime we inhabit on scales ranging from the cosmic horizon
down to the event horizons of suspected black holes, using
photons and astronomical objects as test particles.

2) Some key issues are: (i) the global topology and curvature of
space, (ii) the expansion history of spacetime and evidence for
dark energy, (iii) the fluctuation history of spacetime and
evidence for dark matter, and (iv) strongly curved spacetime and
evidence for black holes.

3) Important constraints on theory arise from the cosmic
microwave background (CMB) (2), gravitational lensing, supernovae
Ia, large-scale structure (LSS), the hydrogen Lyman-alpha forest
(LyF) (3), stellar dynamics, and x-ray binaries. Although it is
fashionable to use cosmological data to measure a small number of
free "cosmological parameters," the author argues that improved
data allow raising the ambition level beyond this, testing rather
than assuming the underlying physics. The author discusses how,
with a minimum of assumptions, one can measure key properties of
spacetime itself in terms of a few cosmological functions -- the
expansion history of the universe, the spacetime fluctuation
spectrum, and its growth.(4,5)

4) In summary: Space is not a boring static stage on which events
unfold over time, but a dynamic entity with curvature,
fluctuations, and a rich life of its own. Spectacular
measurements of the cosmic microwave background, gravitational
lensing, type Ia supernovae, large-scale structure, spectra of
the Lyman-alpha forest, stellar dynamics, and x-ray binaries are
probing the properties of spacetime over 22 orders of magnitude
in scale. Current measurements are consistent with an infinite
flat everlasting universe containing about 30% cold dark matter,
65% dark energy, and at least two distinct populations of black
holes.

References (abridged):

1. E. Einstein, Relativity: The Special and the General Theory
(Random House, New York, 1920)

2. The CMB is the oldest light around, emanating from the hot
opaque hydrogen plasma that filled the universe during its first
400,000 years. An up-to-date review is available from M. White
and J. Cohn, http://arxiv.org/abs/astro-ph/0203120 (2002)

3. The LyF is the plethora of absorption lines in the spectra of
distant quasars caused by neutral hydrogen in overdense
intergalactic gas along the line of sight. It allows us to map
the cosmic gas distribution out to great distances.

4. C. M. Will, Theory & Experiment in Gravitational Physics
(Cambridge Univ. Press, Cambridge, 1993)

5. C. M. Will, http://arxiv.org/abs/gr-qc/9811036 (1998)

ScienceWeek http://www.scienceweek.com

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

6. HISTORY AND FUTURE OF THE UNIVERSE

CONFIRMATION OF BIG-BANG MODEL PREDICTION OF INCREASED BACKGROUND
RADIATION TEMPERATURE AT HIGH REDSHIFT

The following points are made by R. Srianand et al (Nature 2000
408:931):

1) The authors point out that the existence of the cosmic
microwave background radiation is a fundamental prediction of hot
Big Bang cosmology, and the background temperature should
increase with increasing redshift. At the present time (redshift
z = 0), the temperature has been determined with high precision
to be 2.726 +- 0.010 degrees kelvin. In principle, the background
temperature can be determined using measurements of the relative
populations of atomic fine-structure levels, which are excited by
the background radiation. But all previous measurements have
achieved only upper limits, thus still formally permitting the
background radiation temperature to be constant with increasing
redshift.

2) The authors report the detection of absorption lines from the
first and second fine-structure energy levels of neutral carbon
atoms in an isolated cloud of gas at redshift z = 2.3371. The
authors report they also detected absorption due to several
rotational transitions of molecular hydrogen, and fine-structure
lines of singly ionized carbon. The authors suggest these
constraints enable them to determine that the background
radiation was indeed warmer in the past: they find that the
cosmic microwave background temperature at z = 2.3371 is between
6.0 and 14 degrees kelvin, and they point out this is in accord
with the temperature of 9.1 degrees kelvin predicted by hot Big
Bang cosmology.

Related Material:

ON THE EVIDENCE FOR THE BIG BANG MODEL

The following points are made by Martin J. Rees (Science 2000
290:1919):

1) The author suggests that the extrapolation by astrophysicists
and cosmologists back to a stage when the Universe had been
expanding for a few seconds deserves to be taken as seriously as,
for example, what geologists or paleontologists tell us about the
early history of the Earth. Their inferences are just as indirect
and generally less quantitative. Moreover, there are several
discoveries that might have been made over the last 30 years that
would have invalidated the Big Bang hypothesis and which have not
been made:

a) Astronomers might have found an object whose helium abundance
was far below the amount predicted by the Big Bang model -- 23
percent. This would have been fatal to the model, because extra
helium made in stars can readily boost helium above its
pregalactic abundance, but there seems no way of converting all
the helium back to hydrogen.

b) The background radiation measured so accurately by the Cosmic
Background Explorer (COBE) satellite might have turned out to
have a spectrum that differed from the expected *blackbody or
thermal form. Furthermore, the radiation temperature could have
been so smooth over the whole sky that it would be incompatible
with the fluctuations needed to give rise to present-day
structures like the clusters of galaxies.

c) A stable *neutrino might have been discovered with a mass in
the range of 100 to 10^(6) electron volts. This would have been
fatal to the Big Bang model, because the hot early Universe,
according to the theory, should have contained almost as many
neutrinos as photons. If each neutrino weighed even a millionth
as much as an atom, the neutrinos would in toto contribute too
much mass to the present Universe -- more, even, than could be
hidden in *dark matter.

d) The observed deuterium abundance could have been so high that
it was inconsistent with big bang *nucleosynthesis (or so high
that it implied an unacceptable low *baryon density).

The author states: "The Big Bang theory's survival gives us
confidence in extrapolating right back to the first few seconds
of Cosmic history and assuming that the laws of microphysics were
the same then as now."

Notes:

In physics, a "black-body" is an ideal body that absorbs all
radiation and reflects none of it, and black-body radiation is
the emission of radiant energy that would occur from a black-body
at a fixed temperature and with a spectral energy distribution
described by Planck's black-body radiation equation.

Neutrinos are fundamental particles with zero charge, possibly
zero mass, and an angular momentum factor (spin) of 1/2. Various
natural processes produce neutrinos: stellar nuclear reactions,
reactions occurring during supernova explosions, cosmic ray
collisions with matter, etc.

nucleosynthesis: In this context, the fusion reaction in stars
that produce the various elements.

baryon: A baryon is a nuclear particle, e.g., a proton, built
from 3 quarks (fundamental particles that combine to make up
protons, neutrons, and mesons).

ON THE FUTURE OF EARTH AND THE UNIVERSE

The following points are made by Adams and Laughlin (Sky &
Telescope 1998 August):

1) The authors present a view of the future of the universe, the
extrapolation based on the "open" or continuing expansion
universe model, with the authors demarcating various epochs in a
time-span that ranges from the Big Bang to 10^(100) years into
the future.

2) Eventually the stars and galaxies that define our era will
give way to a cosmos of bizarre frozen stars, evaporating black
holes, and lonely atoms the size of galaxies.

3) In roughly 1.1 billion years, according to the current theory
of stellar evolution, our own Sun will heat up enough to make the
Earth inhospitable to life. In 7 billion years, the Sun will
become a full-fledged *red giant star, expanding in size to
nearly engulf the Earth, and certainly melting the Earth's crust
completely and "obliterating every trace of the geology, biology,
and civilizations that once graced the planetary surface." A few
hundred million years after that, the Sun will exhaust its
nuclear fuel, shed its outer layers to become a *white dwarf
star, and begin a slow fade to black.

4) In the time frame of 10^(100) years, the 10 or 15 billion
years already gone by represent an utterly insignificant fragment
of time. The significant entries on the cosmic calendar outlined
by the authors are as follows:

10^(-44) seconds: *Big Bang. The indicated time is the Planck
time, the quantum unit of time itself, and indivisible.

10^(-37) seconds: *Inflation begins.

10^(-34) seconds: Microscopic fluctuations that will become the
seeds of galaxies and clusters of galaxies.

10^(-32) seconds: Inflation ends. An interval of continual
expansion and cooling begins, the Universe dominated by smooth,
uniform, and dense radiation, with stars and galaxies not yet
formed.

10^(-10) seconds: Electroweak phase transition; the
electromagnetic and *weak forces become separate for the first
time.

10^(-5) seconds: *Quarks become confined to form protons and
neutrons.

10^(2) seconds: Synthesis of light elements.

10^(5.5) years: Electrons and protons combine to form hydrogen
atoms. Universe becomes transparent; *cosmic background radiation
breaks free.

10^(6) years: First possible stars.

10^(8.8) years: Formation of galaxies.

10^(10) to 10^(10.1) years: Lifespan of Sun and warm Earth.

10^(17) years: Most planets are detached from stars.

10^(20) years: Most stars and planets have left galaxies.

10^(25) years: Remaining dark white dwarfs absorb and deplete
*weakly interacting massive particles (WIMPS) from galactic
halos.

10^(30) years: *Black holes accrete remaining dark whitedwarfs
and *neutron stars on galaxy-size scales.

10^(33) years: Black holes accrete remaining stars on cluster-
size scales.

10^(37) years: Possible decay of protons. Nothing made of atoms
remains.

10^(44) years: Possible decay of *axions into photons.

10^(46) to 10^(64) years: Black holes the only remaining
concentration of mass.

10^(65) years: Stellar mass black holes evaporate.

10^(83) years: Million-solar-mass black holes evaporate.

10^(99) years: Largest galaxy-mass black holes evaporate; empty
era begins.

10^(108) years: *Positronium formation and decay in a flat
universe.

The authors introduce what they call the "Copernican time
principle". Just as our planet, and hence humankind, has no
special location, the current cosmological epoch has no special
place in the vast expanse of cosmic time. The authors state:
"This principle thus exorcises the last vestiges of
anthropocentric thought."

Notes:

A red giant star is a star in a late stage of evolution, having
exhausted the hydrogen fuel in its core. It has a surface
temperature of less than 4700 degrees Kelvin and a diameter 10 to
100 times that of the Sun.

White dwarf stars are extremely dense and compact stars that have
undergone gravitational collapse. They are the final stage in the
evolution of low-mass stars after they have lost their outer
layers. White dwarf stars are about the size of Earth, but with a
mass about that of the Sun.

The weak force, one of the four fundamental forces, occurs
between leptons (particles without internal structure, e.g.,
electrons, neutrinos) and hadrons (particles with internal
structure, e.g., neutrons and protons); the weak force is
responsible for radioactivity.

weakly interacting massive particles (WIMPS): This refers to a
hypothetical elementary particle that is a candidate for cosmic
dark matter, a stable neutral particle, somewhat heavier than the
neutron, that interacts only weakly with ordinary matter.

If the terminal stages of star death leave a remnant star mass
greater than 3 solar masses, the ultimate gravitational collapse
will produce a black hole, a relativistic singularity. A black
hole is a localized region of space from which neither matter nor
radiation can escape. The "trapping" occurs because the requisite
escape velocity, which can be calculated from the relevant
equations, exceeds the velocity of light and is therefore
unattainable. Another view of a black hole is that it is a mass
that has collapsed to such a small volume that its gravity
prevents the escape of all radiation. Space and time essentially
have no meaning in a black hole. The boundary of the black hole
is called the "event horizon", because any event within the
boundary is invisible outside, the invisibility resulting from
the fact that no radiation can escape to be detected. The radius
of the black hole depends upon how much matter has fallen into
the region; it is called the "Schwarzchild radius", and it is
usually a few kilometers. However, massive black holes are
possible and are thought to be the source of quasars (quasi-
stellar objects), which are extremely luminous sources radiating
energy over the entire spectrum from x-rays to radio waves, and
which are apparently the oldest and most distant objects in the
universe. If quasars indeed involve black holes, the radiation is
from material just outside the black hole, and not from anything
within it. Nothing inside a black hole can get out of it.

If, following its terminal stages, the remnant mass of a star is
between 1.4 and 2 to 3 solar masses, the star will collapse into
a neutron star, a body with a radius of 10 to 15 kilometers, with
a core so dense that its component protons and electrons have
merged into neutrons. The average density of a neutron star is
10^(15) grams per cubic centimeter, and the weight of an object
on the surface of a neutron star would be 10^(11) its weight on
the surface of the Earth. Neutron stars apparently have an outer
shell of iron, but it is iron like no Earth iron, an iron of 4
orders of magnitude greater density. Theory predicts that a
neutron star should rotate very rapidly, be extremely hot, and
have an intense magnetic field. Pulsars, sources of pulsed radio
energy, are evidently spinning neutron stars which emit beams of
radiation from their magnetic poles. A few pulsars have been
found in binary systems, and the empirical estimated masses of
the pulsars are consistent with the masses predicted by neutron
star models.

axions: A hypothetical elementary particle of very low mass and
zero charge, and one of the candidates for dark matter in the
Universe.

Positronium: A positron-electron system that lasts for a
measurable time before combining to produce annihilation
radiation. Positronium can be thought of as an atom analogous to
that of hydrogen in which the electron and positron move in
orbits about the center of mass halfway between them. A positron
is the antiparticle of the electron, with a rest mass equal to
that of the electron, but with opposite charge.

ScienceWeek http://www.scienceweek.com

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

NOTICES

ScienceWeek is a copyrighted publication, and any issue in whole
or in part should not be archived, posted, or distributed by
individual subscribers for use by other persons without
permission.

Information concerning low-cost group subscriptions is available
at http://www.scienceweek.com/groups.htm

ScienceWeek copyright extends only to material originated by
ScienceWeek. Other copyrights may obtain for other material.

CHANGE OF EMAIL ADDRESS: If at any time you need to change the
Email address at which you receive SW, please send the
information to: request@scienceweek.com

SCIENCEWEEK SUBSCRIPTIONS: Information concerning subscriptions
is available at: http://www.scienceweek.com/subinfo.htm

We welcome comments, suggestions, and criticisms from our
subscribers. Editorial contact: editors@scienceweek.com

Editor/Publisher: Dan Agin
Managing Editor: Claire Haller
Associate Editor: Joan Oliner

Copyright (c) 1997-2003 SCIENCE-WEEK
All Rights Reserved

---------------------------------------------

ScienceWeek/Spectrum Press Inc.
3023 N. Clark Street #109
Chicago, 60657-5205 IL, USA.

---------------------------------------------

-----end file