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

**4.3 A Critique of Inflation: Expectations and Performance**

The concept of inflation enjoyed considerable popularity in the first half of the last decade, though this enthusiasm seems to have died down somewhat in recent years. Taking stock of the expectations raised by inflationary scenarios in the light of its actual performance is therefore worthwhile.

Such a discussion falls conveniently into two types of questions:

1. How serious are the original problems that the inflation was invoked to solve? What alternative explanations are possible for these difficulties and how well does inflation perform vis a vis the other solutions?

2. What are new features, good and bad, that inflationary scenarios have introduced into cosmology?

Let us start with the first set of questions. In the original version, inflation was suggested as a possible solution to the horizon, flatness, and monopole problems. Of these, the monopole problem has received considerably less attention in recent literature. The currently favored unified field theories do not lead to a monopole problem. Thus, we concentrate on the flatness and horizon problems.

It is indeed true that inflation does solve these problems if these
problems were stated in a particular form: inflation can suppress the
value of (*kc*^{2} / *a*^{2}) term; it can
also make the observed region of the
last scattering surface (LSS) a causally connected domain. One should
not ignore, however, certain disturbing features in the inflationary
solution to these problems:

Both these problems deal with the initial conditions for our
universe. Since Einstein's equations permit *k* = - 1, 0 or + 1 in a FRW
solution, the value of k needs to be supplied as an extra input to
classical theory. But the creation of the universe (i.e. physics at *t*
< *t _{p}*) needs to be understood quantum mechanically rather than
classically! [It is quite possible that quantum gravitational effects
make a

This anomaly is quite striking when we consider the horizon problem. The horizon problem exists because the integral

is finite. But do we know that it is finite? To make such a claim we
have to assume that there was a singularity at *t* = 0 and that we know
the behavior of *a (t)* arbitrarily close to *t* = 0. For
*t* < *t _{p}*, quantum
gravitational effects will modify the behavior of

Even within the context of the inflationary models, the solutions to
these problems work only for a limited time
(40,
41,
93).
For example,
Ellis has shown how the flatness problem will resurface in the
late-time behavior of a *k* 0
universe. [This should be clear from the
fact that at sufficiently late times, both the *k* = + 1 and
*k* = - 1
models will behave very differently irrespective of the present value
of the (*kc*^{2} / *a*^{2}) term.] In the case
of the horizon problem, it can be
shown that LSS will appear homogeneous only for times *t* <
*t*_{crit} when

[For *t*
10^{-34} s, *t _{f}* 100

Let us now consider the second question, that is, the new features that inflation has brought into cosmology. The major success of inflation in our opinion lies in these factors.

First, inflation has provided a mechanism that allows one, in principle, to compute the spectrum of density inhomogeneities from fundamental physics. This must be considered a success because this is the first time we have a computable mechanism for producing density inhomogeneities.

Also, a definite prediction emerges from inflationary models. The
same mechanism that produces the density inhomogeneities also produces
gravitational wave perturbations. These perturbations also have a
scale invariant power spectrum and an r.m.s. amplitude of about
(*H* / 10^{19} GeV). The energy density of the
gravitational waves
contributes a fraction _{grav}
10^{-5} (*H / m*_{p})^{2}
*h*^{-2} to the critical density,
where *m*_{p} is the Planck mass
(1,
5,
43,
105,
129).
Such perturbations
can induce a quadrupole anisotropy in the MBR. The present bounds on
this anisotropy (
10^{-4}) suggest that *H* < 10^{15} GeV. The value
of _{grav}
can also be restricted by the timing measurements of the millisecond
pulsar; the present bound is _{grav} (
~ 1pc) 3 x 10^{-7}. A positive
detection of quadrupole anisotropy in MBR or a direct detection of
relic gravitational radiation will certainly go a long way toward
boosting confidence in inflation. (The Laser Interferometer Gravity
Wave Observatory (LIGO) and similar projects can, in principle, reach
a sensitivity of _{grav} ~ 10^{-11}.]

Second, several investigations have suggested that inflation could
be a generic feature of cosmology; in other words, for almost any kind
of *V* () and for a large
class of initial conditions, the universe will
undergo a phase of exponential expansion
(63,
64,
112,
116). The
amount of inflation, time of occurrence, etc. can all be quite varied,
but the physical phenomenon is probably here to stay (see, however,
the discussion in Section 6).

The above two features also have a negative side, discussed in
Section 4.2:
Inflation produces too much density inhomogeneity. Every
unworkable model for inflation rules out a parameter range for the
potential *V* () and can, in
principle, constrain particle physics
models. This is probably the most important unsolved problem in the
physics of the early universe.