**2.1. The Standard Big Bang**

To start with, I will introduce the basic tools and ideas of the
standard ``Big Bang'' (SBB) cosmology. Students needing further
background should consult a text such as Kolb and Turner
[2]. An
extensive discussion of inflation can be found in
[3].
The SBB treats a nearly perfectly
homogeneous and isotropic universe, which gives a good fit to present
observations. The single dynamical parameter describing the broad
features of the SBB is the ``scale factor'' *a*, which obeys the
``Friedmann equation''

in units where *M*_{P} =
= *c* = 1,
is the energy density
and *k* is the curvature.
The Friedmann equation can be solved for *a(t)* once
(*a*) is
determined. This can be done using local energy conservation, which
for the SBB cosmology reads

Here (in the comoving frame) the stress energy tensor of the matter is given by

In the SBB, the Universe is first dominated by relativistic matter
(``radiation dominated'') with *w* = 1/3 which gives
*a*^{-4} and *a*
*t*^{1/2}. Later the Universe is dominated by
non-relativistic matter (``matter dominated'') with *w* = 0 which
gives
*a*^{-3} and *a*
*t*^{2/3}.

The scale factor measures the overall expansion of the Universe
(it doubles in size as the separation between distant objects
doubles). Current data suggests an additional ``Cosmological
Constant'' term
/ 3 might be present on the
right hand
side of the Friedmann equation with a size similar to the other terms.
However with the and
*k* terms evolving as
negative powers of *a* these terms completely dominate over
at the earlier epochs we are discussing here. We
set = 0 for the rest of this
article.