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''

(1)

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

(2)

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

(3)

In the SBB, the Universe is first dominated by relativistic matter (``radiation dominated'') with w = 1/3 which gives a<sup>-4</sup> and a t<sup>1/2</sup>. 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.