**1.5. = 1, Dark
Matter and Inflation**

There is no compelling direct observational evidence for
_{0} = 1. The
driving force behind the notion that
_{0} = 1 is
undoubtedly the
inflationary picture for the early universe (see the review of
Brandenburger, 1990).
Not only does this picture have appeal in
providing answers to some fundamental questions (like the horizon
problem), but it seems almost inevitable from the point of view of our
present knowledge of high energy physics. That weighs more strongly in
favour of adopting
_{0} = 1
than the lack of any obvious candidate
particle weighs against the notion.

It is interesting to write down and solve the equation for the
evolution of the density parameter
(*t*) with time
(Ducloux, 1989).
Suppose the matter in the universe has density
and
pressure *p* such that

The case *p* = 0,
= 1/2 is relevant to the current epoch, while the
radiation gas case
*p* = 1/3*c*^{2},
= 1 is
relevant to the early
universe. The interesting very early universe case
*p* = -
*c*^{2} corresponds to
= - 1.

A not inconsiderable amount of work gives the evolution of as

The simplest case = 1 is relevant to the current era and the solution is then trivial:

Thus in order to get
_{0} = 0.1
today, we need
_{P} = 1 -
10^{-60} at the Planck time
*t*_{P} ~ 10^{-60}*t*_{0}. It is the
fact that should
have been so
incredibly close to 1.0 initially that is referred to as the "fine
tuning" problem. The argument goes then that it was so close it must
(sic) have been exactly 1.000 ... . The alternative is to seek a
mechanism whereby such a value might be generated. The mechanism is
"inflation".

In its simplest form the idea of inflation is as follows. If at an early stage the universe had equation of state

the cosmic expansion would be exponential:

The fact that the pressure *p*_{V} is negative is a
consequence of the
physics of the vacuum at the high temperatures prevailing in the early
universe.

The exponential expansion phase is referred to as the "de Sitter phase" and would continue for as long as the material had this peculiar equation of state. The universe then makes a transition to an expansion for a "normal" equation of state. It turns out that during this "de Sitter" expansion phase, very distant parts of the universe are causally connected. This is presumed to be an "explanation" for the flatness problem, the idea being that all anisotropies and inhomogeneities disappear during this phase of phenomenal expansion.

The other side of the coin is that it is necessary to generate some primordial inhomogeneities that will eventually give rise to the formation of galaxies and large scale structure. These must be generated during or after the inflationary era and are generally thought to arise out of quantum fluctuations in the vacuum state. In the simplest models the spectrum of fluctuations is the Harrison-Zel'dovich spectrum with Gaussian distributed fluctuations (Guth and Pi, 1985). We now appear to have evidence that this spectrum does not have enough large scale power to explain the observations of large scale structure. (See Kashlinsky and Jones (1991) for arguments that the spectrum is not Harrison-Zel'dovich).

There is however no lack of alternate (albeit somewhat *ad hoc*) model
which allow us to get around the problem of the lack of large scale
power in the Harrison-Zel'dovich spectrum. One of the most plausible
ways around this is by generating non-Gaussian fluctuations. Chaotic
inflation
(Linde, 1984,
Linde and Mukhanov, 1987)
can generate
non-Gaussian fluctuation
(Matarrese, Ortolan and
Lucchin, 1989;
Yi, Vishniac and Mineshige,
1991).
Strong claims have been made for models
involving "global texture" as these also generate non-Gaussian initial
fluctuations
(Spergel et al., 1991).