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OCR for page 90
1z
Highlights
BIG-BANG NUCLEOSYNTHESIS
At present, the relics of the big bang that provide the most informa-
tion about the early universe are certain light nuclei, such as deuterium
(D) and 4He. Calculations of their production in the early universe are
based on measured nuclear cross sections and rely heavily on quanti-
tative details of the cosmological model. A few minutes after the origin
of the universe, conditions of temperature and density were appropri-
ate for the fusion of protons and neutrons to form nuclei of light ele-
ments. Deuterons formed first, but the fusion reactions ran rapidly
toward 4He because of its much greater stability. The amount of 4He
produced depends essentially on two factors: the density of baryons
(neutrons and protons) and the universal expansion rate at the epoch
when the temperature dropped to ~109 K (t ~ 3 min). The baryon
density at T~ 109 K can be computed from the present baryon density
and the present temperature of the background radiation; and the
expansion rate can be calculated for isotropic, homogeneous cosmo-
logical models provided that the number of species of light particles is
known. Hence precise predictions of the 4He abundance can be made;
the calculated value lies in the range of 23-27 percent by mass. This
agrees with the solar value and with the abundance found on old stars
and in the interstellar medium, after correcting for the 4He made in
stars. The fact that the predicted abundance of 4He agrees with the
90
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HIGHLIGHTS 9 1
RAT 10 OF BARYONS TO PHOTONS
10-'° 10-9 lo-8 10-7
.26
.22
.18,
10-31
~ 10 5
11
c'' 10 7
In
Cat
10 9
10"
_ 4He
- Few
Observed
~ Pred i cted
_ ~ D+3He
_ ~
_ .
1 _ ~ ~
- AL;
, , _
3He
\D
\~
0-32 1 o-3
10-32 10-31 10-3° lo-29 10 28
PRESENT BARYON DENSITY (g/cm3)
FIGURE 12.1 Isotopic abundances compared with predictions of the standard big-bang
model (black curves). Shaded areas indicate observed abundances for 4He, deuterium,
3He, and 7Li, which all show remarkable agreement with theory for a baryon-to-photon
ratio in the range 10-'° to 10-9.
Observed value provides the best evidence for the validity of the
standard big-bang model at these early times.
Even more has been learned from studies of light-element abun-
dances. While the 4He abundance is not a strong function of the density
of baryons, the small residual D abundance depends sensitively on this
quantity, being relatively larger for lower baryon density. Figure 19. 1
shows the predicted primordial abundances of several light nucleic as
functions of the present baryon density- a poorly known cosmological
parameter. The observed abundances are shown by shaded rectangles,
with 7Li being a recent addition. The agreement with predictions is
striking and suggests a present baryon density of 3 x 10-3 g/cm3. This
OCR for page 92
92 COSMOLOG Y
density is 1 or 2 orders of magnitude less than the density required to
close the universe, that is, to stop the current expansion and cause
recollapse. It also may be less than the density required to explain the
observed dynamics of large clusters of galaxies. Thus, suspicion is
rising that the long-sought invisible (sometimes called missing or dark)
matter is something other than baryons. We return to this point below
in the section on Invisible Mass.
One might suppose that the observed light nuclei were produced by
much later astrophysical processes, making the agreement in Figure
12.1 fortuitous. At this point we know that these light nuclei cannot be
produced by the collisions of cosmic rays with the interstellar gas and
that no other production mode has been found for D. Thus, the
deuterium abundance is particularly important.
The sensitivity of the production of 4He to the expansion rate of the
universe at t ~ 3 min has allowed constraints to be placed on other
physical parameters. For instance, if more than a few types of neu-
trinos exist, the expansion rate would have been greater, resulting in
excessive production of helium. Also, if the gravitational "constant"
had been different at that early epoch (G/G ~ 0), the expansion rate
and the helium production would have been altered. Finally, the uni-
verse could not have been very anisotropic at t = 3 min. because that
would also have increased the average expansion rate.
LARGE-SCALE PROPERTIES OF THE UNIVERSE
The general expansion and deceleration rates of the universe have
been a central focus of cosmology for the past 30 years. Recent work
has narrowed the uncertainty in Hubble's constant, a measure of the
current expansion rate (Ho = 50 to 100 km/s per Mpc*), but the
deceleration parameter q0t remains poorly known. The classical meth-
ods to study the geometry of space-time use visible galaxies and radio
sources as coordinate measures. Usually, source intensity is used as a
measure of distance, but this requires a knowledge of time dependence
of the source luminosity and spectrum. The effects of source evolution
have not yet been sufficiently well understood to permit a geometrical
* 1 megaparsec (Mpc) ~ 3 x 106 light-years, roughly 1/5 the spacing between large
galaxies.
t In the simplest big-bang models (pressure = 0, cosmological constant = 0) q0 =
t/2Pmeasure~/Pcri~ica~. For q ~ 1/2 the universe is open and expands forever; q > 1/2 means
our universe is closed and will recollapse. Measurements of the density p and deceler-
ation qO of the universe are of major importance to cosmology.
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Representative terms from entire chapter:
baryon density
Lo
~ ~ -
HIGHLIGHTS 93
FREQUENCY (G He
40 4
. . . . . .
MICROWAVE BACKGROUND
SPEC T R U M
_ 10 14 _
:r
-
-
~n
~ 10 46
cot
cot
94 COSMOLOGY
at that epoch. Einstein's major cosmological assumption of large-scale
homogeneity and isotropy seems well justified.
Incidentally, there is an interesting noncosmological feature in the
anisotropy of the 3-K radiation- the dipole erect. It arises from the
Earth's motion through the radiation and measures our velocity
relative to the reference frame of the radiation, assumed to be the same
as that of matter at large distances. The inferred velocity of our galaxy
is surprisingly large and suggests that we are being perturbed by local
mass concentrations such as the Virgo cluster of galaxies and its
surroundings.
Failure to observe a quadrupole anisotropy with an amplitude larger
than 10-4 K provides an important constraint on homogeneous but
anisotropic cosmological models. Such models are completely consis-
tent with general relativity, and indeed the number of such models is
much larger than the number of isotropic models. Nevertheless, ob-
servations of the isotropy of the background radiation, and the
agreement of the predicted and measured abundances of light-element
abundances, tightly restrict the range of possible anisotropic models.
Finally, the high degree of isotropy in the 3-K radiation raises a
serious causality question. In the standard model, regions separated in
the sky by more than ~1 degree were not yet causally connected at
z ~ 103, the epoch of last scattering (assuming no reionization). How
then did the photons coming from those regions manage to have the
same temperature, to 1 part in 104? This long-standing problem with the
3-K radiation in the simple model may be solved by a fascinating new
idea the inflationary universe discussed below in the section on The
Inflationary Universe.
STRUCTURE IN THE UNIVERSE
The clumping of matter in the universe into galaxies, clusters of
galaxies, and still larger structure is currently under intense scrutiny.
Quantitative observational work has rapidly accelerated with new
developments in detector and data-processing technology. Analyses of
angular distributions of galaxies on photographic plates are now
complemented by three-dimensional information from the first large-
scale statistical samples of galaxy redshifts.* Redshift measurements
require spectra, so they take much more time to obtain than do
* The redshift gives the recession velocity, which is related to the distance by
Hubble's law v = Hod.
HIGHLIGHTS 95
photographs, but redshift surveys yield a much clearer picture of the
galaxy distribution and dynamics. On small scales (~10 Mpc) the
galaxy distribution approximates a scale-invariant fractal within which
there is an occasional great cluster of galaxies. On larger scales one
finds a complex pattern of superclusters, clouds, voids, and filaments
of galaxies. There is considerable theoretical and observational activity
devoted to tracing the evolution of this structure back to its origins.
Evidence exists that radio sources, quasars, and perhaps also galaxies
have changed appreciably between the epoch z ~ 3 and the present.
But the burst of radiation that may accompany galaxy formation at an
epoch somewhere between z ~ 3 and z ~ 100 has not yet been seen.
Indeed, so little is known about the formation and development of
structure in the universe that we are currently debating whether stars
or large clusters of galaxies formed first.
Galaxies and clusters of galaxies may arise from small density
fluctuations, Ap/p, in the early universe. Two limits can be set on the
magnitude of fluctuations at the time of decoupling of matter and
radiation. Since the current density contrast on the scale of clusters of
galaxies is about unity, and gravity causes Pip to grow as (1 + z)-i,
the perturbations at z ~ 103 should be pip ~ 10-3. Another limit
comes from the search for small-scale anisotropy in the 3-K radiation,
which is a probe of roughness on the z ~ 103 surface. At angular scales
corresponding to the sizes of large clusters (a few arc minutes) no
fluctuations are seen down to ATIT~ 2 x 10-5. Current results of
isotropy measurements of the 3-K radiation are shown in Figure 12.3.
Under certain assumptions about the character of the fluctuations
these two ways of estimating Ap/p are in conflict. For example, adi-
abatic perturbations (favored by some models, especially those derived
from particle-physics considerations) give pip ~ 3AT/T. Then the
density contrast seen today Pip ~ 1) implies ATIT~ 3 x 10-4 at z ~
103. But the limits shown in Figure 12.3 at scales of a few arcminutes
are ten times smaller. There are several ways out of this dilemma:
make the perturbations isothermal, clump the matter by forces other
than gravitational (e.g., by supernova explosions), or rescatter the 3-K
photons from an intermediate screen of electrons at z ~ 103. A recent
idea suggests that nonbaryonic, invisible matter (e.g., anions,
photinos, or massive neutrinos) can become nonrelativistic and begin
to clump before z ~ 103. Baryons then fall into these clumps after
decoupling from the radiation. Thus, there is ample time for structure
to form in the invisible matter, and baryonic matter and microwave
photons can be very weakly perturbed at decoupling.
This is only one of the many ways that newly suggested particles
96 COSMOLOG Y
lo-3
- lo 4
10-5
Anisotropy of 2.7 K Radiation Dipole
( 95 % Conf i dence Leve I s ) ~
~ \
10 30 1 3
· \
\ /
~ \ ~
T/? 1? ~ ~ ~
l l ll
1 0' 301 1 ° 3°
,,, , I 1 1,
1 0 ° 30° 90° 180°
Angular scale
10
1.0
0.1<
.01
FIGURE 12.3 Current results of searches for anisotropy in the cosmic microwave
background radiation. The only effect seen, so far, is the dipole, which is due mainly (and
perhaps totally) to our velocity through the radiation. Various symbols denote different
observational techniques. Generally, small balloonborne instruments are used at angular
scales larger than 3 degrees' and ground-based radio telescopes are used at smaller
angular scales.
.
have been used to try to solve certain cosmological problems. On the
other hand, the universe is a good laboratory in which to try out the
properties of new particles. For example, the various candidates for
invisible matter have different clustering properties. Some can form
seeds for structures in the matter; others can provide a smooth mass
density to help close the universe. Thus, cosmological observations
can place constraints on the properties and abundances of new kinds of
particles.
INVISIBLE MASS
The dark-matter problem is not new to cosmology. Observations
since the 1930s have indicated that the mass density of visible matter
(stars and gas) is insufficient to close the universe or to explain the
dynamics of large clusters of galaxies, and recently it has become
apparent that the visible mass cannot account for the strength of the
gravitational field in the outer parts of galaxies, as indicated by the
motions of stars and by the concentration of plasma around some
galaxies. The discrepancy between what is observed directly as visible
mass and what is indicated by dynamical measurements ranges from a
factor of 2 in our stellar neighborhood to a factor of about 5 in galaxies
HIGHLIGHTS 97
to a factor of 30 or more in clusters of galaxies. This interesting trend
for the invisible-mass fraction to increase with scale is not understood.
With so much at stake, the search for the invisible mass is vigorous
and extensive. Low-mass stars (mass ~ 0.1 MSun) are now unlikely
candidates because galactic halos do not exhibit excess brightness at
A = 2 ~m, where such stars are bright. Still lower mass objects
("Jupiters") are possible, since they are not luminous and hence are
extremely hard to detect.
Black holes are popular candidates for the invisible mass; and again,
they are hard to find, especially in isolation. Currently, we are not even
agreed that a black hole has been identified, though there are several
excellent candidates among the known x-ray sources. Massive black
holes (~108 MSun) are suspected as the "central engines" in active
galaxies and quasi-stellar sources. Also, primordial black holes with
masses down to 1O'5 g could exist and easily have escaped detection.
(Those with masses below ~ 10'5 g are predicted to have evaporated by
now by the Hawking process; see section on Quantum Particle
Creation by Black Holes in Chapter 8.) Theoretical studies have taught
us much about the astrophysical and relativistic properties of black
holes, but we still do not understand how (if at all) such objects act as
the powerhouses for active galactic nuclei or whether it is reasonable
to assume that black holes might have existed in great numbers in the
early universe. Their contribution to the invisible mass remains un-
known.
Since the dark-matter candidates mentioned so far are made from
baryons, the nucleosynthesis constraint on baryon mass density has
strong implications here. Stars, "Jupiters," and even black holes born
after big-bang nucleosynthesis are included in the baryon density
constraint noted in Figure 12.1- a density far short of that needed to
close the universe. Thus, nucleosynthesis argues that one should look
for nonbaryonic dark-mass candidates as a means to achieve closure
density, Pc ~ 10-29 g/cm3.
Several, yet unobserved, elementary particles are being proposed as
dark-matter candidates. Already before reports of measured neutrino
mass came from the Soviet Union, cosmologists had speculated about
massive neutrinos as a source of nonbaryonic mass density. If neutri-
nos have a rest mass of only a few electron volts, the thermal neutrinos
produced in the hot big bang would dominate the mass density of the
universe today. Although the reported measurement of neutrino mass
is still controversial, it ushered in a flurry of theoretical activity
resulting in even more invisible mass candidates. Axions were men-
tioned earlier as possible seeds for galaxies; they are light pseudo-
98 COSMOf OGY
scalar particles produced during the transition from quarks to hadrons
that preceded primordial nucleosynthesis. Other new candidates are
suggested by supersymmetric particle theories, which give partners
such as the photino and gravitino to currently known particles.
The virtually unconstrained richness of particle theory at very high
energies can be expected to breed many invisible matter candidates.
However, some constraints do exist. To help bind galaxies a relic par-
ticle must have sufficient abundance today and must have become
nonrelativistic so that gravitational clumping could take place. Also,
the mass of any fermion candidate must be greater than the phase-
space limit provided by the exclusion principle. ~ Some proposed
particles have natural clustering scales that can be compared to
observed structure, but it is still controversial which clustering lengths
give the best fit to the phenomena.
COSMOLOGY AND GRAND UNIFICATION
A recent dramatic development in theoretical physics was the
realization that the early universe is a useful laboratory for the testing
of particle physics; conversely, new ideas in particle physics can be
applied to some fundamental cosmological questions. Most interest has
focused on an epoch when temperatures were high enough (T—1027 K
or 1015 GeV) to possibly induce grand unification of three fundamental
forces the strong, the weak, and the electromagnetic. An early suc-
cess of this idea was to provide a possible explanation of the puz-
zling asymmetry in the abundance of matter and antimatter in the
universe, amounting to about one excess baryon (matter) per 109
photons. The standard cosmological model gives no clues, but Grand
Unification Theories (GUTs) contain the necessary ingredients to
answer this fundamental question. GUTs can be asymmetric with
respect to particles and antiparticles, and they violate baryon conser-
vation, producing a net baryon number in a universe that initially had
equal numbers of baryons and antibaryons. The process occurs at a
temperature corresponding to the rest-mass energy of the X boson (see
Figure 11.1 in Chapter 11) which is responsible for the interconversion
of quarks and leptons. Currently, particle experiments do not constrain
the parameters of these theories nearly enough to allow an exact
prediction of the baryon-to-photon ratio, although the detection of
* Roughly, m4 > p~3 V-3, or m > 20 eV for typical densities and velocities inside a
galaxy.
HIGHLIGHTS 99
proton decay would at least provide evidence that grand unification
does occur at high energy. Thus, particle theory has provided a
possible physical explanation for a fundamental cosmological property
previously assigned to arbitrary initial conditions.
Another important consequence of GUTs is the possibility of pro-
ducing magnetic monopoles from singularities in the scalar (Higgs)
fields invoked to generate particle masses. This could have occurred at
the GUT era in the early universe, as regions with arbitrary alignments
of the Higgs fields came into causal contact. In fact, in the simplest
big-bang models far too many monopoles would have been produced;
their present mass density would dominate the universe and cause
excessive deceleration of its general expansion. This problem may be
solved by a revolutionary idea that introduces into the early universe a
process called inflation.
THE INFLATIONARY UNIVERSE
An ingenious way has been found to avoid the problem of excess
magnetic monopoles emerging from the GUT era and to explain some
older cosmological puzzles as well. The idea is that if scalar fields exist,
their vacuum expectation value could provide a contribution to the
mass density that remains constant in time, like the effect of the
cosmological constant first introduced by Einstein. During the time
following the GUT era when vacuum expectation energy dominates,
the universe expands much faster than in the usual big-bang models,
and this exponential expansion drastically dilutes the density of
monopoles. The inflationary epoch must terminate, at least by the time
of primordial nucleosynthesis, so that big-bang cosmology reigns
during its successful epochs. According to current ideas, inflation ends
when a lower (zero) energy state becomes accessible to the scalar fields
as the universe cools by expansion.
As noted earlier a particularly vexing problem with simple big-bang
models is that regions of the universe having the same properties
(radiation temperature, for instance) have never been in causal contact
at the time we observe them. To explain the observed uniformity, one
can invoke special initial conditions or quantum processes in the
mysterious Planck era' but the inflationary model provides a specific
alternative mechanism. In this picture, our entire observable universe
is embedded in a larger region that grew from a single causally
connected piece during the era of exponential expansion.
Inflation also provides a possible way of understanding the flatness
question, which basically asks: Why is the universe so close to a
100 COSMOf OGY
balance between its kinetic energy of expansion and its gravitational
binding energy? Considering the huge range of densities encompassed
by the expansion, exceedingly fine tuning of this energy balance was
required to allow the universe to reach its current state. The inflation
picture explains this, again because of the enormous expansion factor.
Indeed the model predicts a flat universe, which (for zero cosmological
constant) has the current mass-energy density in the universe exactly
equal to Pc, the critical closure density. At present, the study of the
inflationary class of big-bang models is one of the most exciting areas
within the rapidly growing union of theoretical particle physics and
cosmology. But experimental support is needed; the discovery of the
Higgs particles that produce the vacuum energy, for instance, would
place inflation on much firmer ground.
GRAVITATIONAL LENSES
In 1979, an example of the long-predicted gravitational tensing was
discovered. Multiple images of a quasar were formed by the bending of
light in the gravitational field of an intervening group of galaxies. Such
alignments are not so rare as one might think, because of the extreme
distances to the quasars; six examples have been found to date.
Cosmologists are intrigued because detailed geometric-optics calcula-
tions of the paths have led to the possibility that the distribution of
mass within the tensing system can be studied. In addition, if the
quasar's luminosity varies with time, the different delays along the
paths to the different images provide an additional scale, which in
principle allows a determination of the distance to the intervening
galaxies and thus the Hubble constant, Ho (see section above on
Large-Scale Properties of the Universe). However, it may prove
difficult to determine the properties of the tensing system well enough
to realize this additional payoff.
