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**1.6.3 Inflation and the Origin of Fluctuations**

Thus far, it has been sketched how inflation stretches, flattens, and smooths out the universe, thus greatly increasing the domain of initial conditions that could correspond to the universe that we observe today. But inflation also can explain the origin of the fluctuations necessary in the gravitional instability picture of galaxy and cluster formation. Recall that the very existence of these fluctuations is a problem in the standard Big Bang picture, since these fluctuations are much larger than the horizon at early times. How could they have arisen?

The answer in the inflationary universe scenario is that
they arise from quantum fluctuations in the inflaton field
whose vacuum energy drives
inflation. The scalar
fluctuations during the de Sitter phase are of
the order of the Hawking temperature *H* / 2. Because of these
fluctuations, there is a time spread *t*
/ during which
different regions of the same size complete the transition to the Friedmann
phase. The result is that the density fluctuations when a
region of a particular size re-enters the horizon are equal
to _{H} ( / )_{H}
~ *t* /
*t _{H}* =

Thus *inflationary models typically predict a nearly constant
curvature spectrum* _{H} = constant
*of adiabatic fluctuations*. Some time ago
Harrison (1970),
Zel'dovich (1972),
and others had emphasized that this is the only scale-invariant
(i.e., power-law) fluctuation spectrum that avoids trouble
at both large and small scales. If
_{H}
*M _{H}*

Inflation predicts more: it allows the calculation of the value of the
constant _{H} in
terms of the properties of the scalar potential
*V*(). Indeed, this proved to
be embarrassing, at least
initially, since the Coleman-Weinberg potential, the first potential
studied in the context of the new inflation scenario, results in
_{H} ~ 10^{2}
(Guth & Pi 1982)
some six orders of magnitude
too large. But this does not seem to be an insurmountable difficulty;
as was mentioned above, chaotic inflation works, with a sufficiently
small self-coupling. Thus inflation at present appears to be a
plausible solution to the problem of providing reasonable cosmological
initial conditions (although it sheds no light at all on the
fundamental question why the cosmological constant is so small now).
Many variations of the basic idea of inflation have been worked out,
and the following sections will discuss two recent developments
in a little more detail.
Linde (1995)
recently classified these
inflationary models in an interesting and useful way: see
Table 1.7.