Annu. Rev. Astron. Astrophys. 1991. 29:
325-362
Copyright © 1991 by Annual Reviews. All rights reserved |

Observations indicate that our universe may contain a large amount of nonluminous, ``dark'' matter. Inflation adds an interesting new dimension to this issue.

In the noninflationary cosmologies, there is no preferred value for
the density parameter . This
quantity was treated by most astronomers
as an input from observations into the theory. Inflationary models,
however, make a very definite prediction about : In the usual
scenarios, = 1 +
*O*(10^{-4}) [the correction of *O*(10^{-4})
arising because
of the fluctuations in the curvature induced by density
inhomogeneities]. This prediction can be tested in two ways: First,
this constraint, added to the fact that the universe is
matter-dominated today, implies that
*H*_{0}*t*_{0} = (2/3). If, based on
stellar and galactic ages, we take *t*_{0} = (12-20) Gyr,
we have to rule
out values of *h* greater than 0.65. An independent determination
of *H*_{0}
leading to, say, *h* 0.65
will rule out inflation.

More directly, inflationary models can be ruled out if observations conclusively point out a value of < 1. Since luminous matter in the universe contributes far less than unity, one may say that the inflationary idea can be correct only if there exists some form of dark matter in sufficient quantities.

The observational status of the value of is not very certain. The following claims have been made in the literature (for a review, see 13, Ch. 10, 100, 115):

The mean density in the solar neighborhood gives about 0.003

*h*^{-1}.Studies based on the Magellanic stream and timing arguments in local groups give a higher value of about 0.06

*h*^{-1}.The mass density in groups of galaxies contributes about 0.16 and that in large clusters give about 0.25.

The Virgo centric fall also suggests a mass density of 0.25.

The constraints from primordial nucleosynthesis imply a constraint on the baryonic contribution to mass density:

_{B}= (0.014-0.026)*h*^{-2}; or if we take 0.5 <*h*< 1, we get 0.014 <_{B}<0.104. (Authors differ somewhat on the upperbound on_{B}and the cited values are in the range 0.1 to 0.2; 69.)

Two features stand out in the above estimates if they are all
correct. First, there seems to be a tendency for to increase with
the scale over which it is measured. (This conclusion is somewhat
tentative and quite controversial.) If we use gravitational effects
occurring in a system of size *L* to measure , we will miss out on
matter distributed smoothly over sizes significantly larger than *L*;
thus, if the universe has a significant fraction of mass distributed
smoothly over scales larger than, say 50 Mpc, we can still reconcile
the above observations with =
1. Second, the observations are just
marginally consistent with a fully baryonic universe with _{B} 0.2 if
(and only if) *h* = 0.4. Thus, these observations alone probably do not
rule out a completely baryonic universe (yet!).

Inflation makes definite claims regarding the above situation. First, inflation is not compatible with a purely baryonic universe (since < 0.2). Thus not only does inflation demand dark matter, it demands nonbaryonic dark matter. Second, inflation requires most of the dark matter (a fraction of about 0.75) to be distributed smoothly at scales larger than about 20 Mpc or so, to escape small-scale bounds on .

Non-baryonic dark matter may be needed for a completely different
reason. As discussed above, perturbations in the baryonic matter are
constrained to be less than about 10^{-4} at decoupling. This does not
give sufficient time for these perturbations to grow into the
structures we see today. The constraints on non-baryonic matter, which
does not couple directly to radiation, are often less severe. Dark
matter perturbations can grow by a factor of at least
(*T*_{eq} / *T*_{dec}) from
the epoch of matter domination till the time of decoupling. Baryonic
matter can be allowed to ``catch up'' with dark matter perturbations
after the decoupling. This can reduce the (*T / T*) value by a factor of
about 50-100 or so in many models (e.g.
109).
A model for galaxy
formation incorporating these constraints is not very easy to build,
however. If we assume that the dark matter is made of weakly
interacting massive particles (WIMPs), we can broadly distinguish
between two scenarios for structure formation depending on the mass
*m _{x}* of the WIMP.

The growth of structures in a universe dominated by a non-baryonic
dark matter particle of mass *m _{x}* proceeds as follows:
These particles
will become nonrelativistic at a temperature

Candidates for dark matter with *M*_{FS} *M*_{eq}
(i.e. for *m _{x}*
100 eV) are
called

For *m _{x}*
100 eV (hot dark matter), the first structures that form
contain masses of about 10

If WIMPs have considerably higher mass [say *m _{x}*

Several attempts have been made to reconcile cold dark matter (CDM)
scenarios with inflation. This can be done (for example) by invoking a
very smooth contribution _{smooth} = 1 - _{CDM}
0.8 due to some relativistic particle
(85,
95,
117),
or, more brazenly, by postulating
a cosmological constant of the required magnitude. All alternative
would be to produce a scenario in which galaxy formation is
``biased'' - i.e. only very overdense regions (3 peaks) lead to the
galaxies we see
(9,
65).
The more numerous, 1-peaks will be
distributed ill a relatively smoother fashion. No final consensus has
emerged regarding these ideas and none of them appears to have a
compelling simplicity or naturalness.

In conclusion, it is worth pointing out one loophole in the
conclusion = 1 in an
inflationary scenario. If there is a residual
-term, then =1 need not correspond to *k*
= 0. Should it turn out
that the FRW models with *k* = 0, = 1 are inconsistent with data, the
inflationary scenario can still survive with a nonzero , although
such a formula for survival would have been purchased dearly at the
cost of simplicity and Occam's razor.

We next discuss the role of the -term in the context of inflation.