We shall not discuss all of the cosmological implications here. The ones
that are perhaps the most important are a detailed picture of the
spontaneous birth of the Universe and the perturbations that led to the
present-day structure (galaxies, clusters, and other density
fluctuations). The spontaneous birth of the Universe, the inflationary
expansion, and the subsequent evolution of the Universe remain unclear and
warrant another review (or rather several reviews). So what follows is
two short remarks having a direct bearing on the scalar field theory.
The first concerns the hypothesis of an eternally bouncing Universe.
Consider a closed Universe whose expansion is limited by some
*a*_{max}
greater than 10^{28} cm (the region that is now observable). In the
simplest case, collapse will follow the expansion. At some instant of
time (long after 2 x 10^{10} years, the present age of the
Universe), the
collapse becomes catastrophic and gives rise to infinite density. Can this
collapse be reversed and give birth to a new cycle, similar to that which
we now observe? There are several arguments (beginning with Tolman's
remark concerning the irreversible growth of entropy) against this
picture of the Universe. We shall not repeat these arguments here. But
new hope for this arose in connection with the existence of formal
symmetric bouncing solutions in scalar field theory. In particular, the
Higgs field with

yields a solution

A reasonable *V*_{max} (corresponding to very heavy
*X* mesons), on the
order of (10^{14} GeV)^{4} in
= *c* = 1 units,
would lead to an
*H*_{0} = 10^{9}.GeV =
10^{35} s^{-1} and an *a*_{min} =
*c/H*_{0} = 10^{-25} cm in the usual units.

But an analysis of the behavior of the scalar field during compression and expansion shows that this picture is very improbable.

= 0, *V* =
*V*_{max} is the only solution in the compression stage. The
general solution is ^{2}
>> *V*(), *p* =
+, which leads
to irreversible
collapse (*a(t)* = (*t*_{0} -
*t*)^{1/3}), at least in
the classical, homogeneous case.
^{(12)}

The argument against periodic repeating cycles of expansion and collapse is an argument in favor of the spontaneous birth of the Universe. For a detailed discussion of the spontaneous birth of the Universe, we refer the reader to the proceedings of the October 1984 Moscow symposium (Quantum Gravity 1984); for an earlier attempt, see Grishchuk and Zel'dovich (1982). Here, we shall only stress that inflationary expansion is necessary in the overall picture. This is a third argument, closely related to the two arguments of Guth (1981) (horizon and flatness), but not identical.

Assume that the Universe was born with a radius equal to the Planck
radius (10^{-33} cm) and a density equal to the Planck density
(10^{93} g cm^{-3}). Then assume that the expansion
proceeds without inflation, like a plasma
(_{r}
*a*^{-4}) or
simple dust (_{d}
*a*^{-3}).

What is the density we should have at present, when *a*
10^{28} cm? Simple arithmetic yields

These numbers are completely unacceptable - the present density of
the Universe is on the order of 10^{-30} g cm^{-3}.

This is a crude but weighty argument that shows that an inflationary
phase with constant (or approximately constant) density during very
strong expansion (a factor of ~ 10^{30}) is necessary. This can
be provided by the scalar field, with its peculiar
- equation of
state. ^{(13)}

This is why an astronomer should read this oversimplified story of the scalar field. The responsibility for the English remains my own.

Thanks to Professors L. P. Grishchuk and L. B. Okun' for discussions and to L. V. Rozhanskii for assistance.

Let us now return to the astronomer described in the introduction who works with telescopes but wishes to have a broader understanding. I do not pretend to give you the ultimate answer - it is not yet known. But perhaps you now know something about the language highbrow theoreticians use to talk about the early Universe. But even this modest goal has only been partially achieved. Alas, the ultimate topic - the very birth of the Universe - remains out of reach of even the highest brow.

^{12} High temperature helps maintain
= 0, *V* =
*V*_{max} during expansion. But it does not
help prevent collapse during compression.
Back.

^{13} Another variant exists, where the
negative pressure is due to the polarization of the vacuum (see
(Starobinskii 1980)).
This subject is too complicated to
treat here, but we hope to return to it in another review paper.
Back.