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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''

Equation 1 (1)

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

Equation 2 (2)

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

Equation 3 (3)

In the SBB, the Universe is first dominated by relativistic matter (``radiation dominated'') with w = 1/3 which gives rho propto a-4 and a propto t1/2. Later the Universe is dominated by non-relativistic matter (``matter dominated'') with w = 0 which gives rho propto a-3 and a propto t2/3.

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 ident Lambda / 3 might be present on the right hand side of the Friedmann equation with a size similar to the other terms. However with the rho and k terms evolving as negative powers of a these terms completely dominate over Lambda at the earlier epochs we are discussing here. We set Lambda = 0 for the rest of this article.

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