Evolution of the universe during the inflationary epoch
  We often find in the literature solutions to the Friedmann and fluid
equations for simple cosmological models during the matter, radiation or
cosmological constant dominated epochs. However no solutions appear for the
inflationary era dominated by the potential energy of a scalar field due,
perhaps, to the fact that we do not have as yet a strongly favored model of
inflation; there are, of course, very well motivated models which fit the data.
The purpose of this article is to study with some detail the evolution of the
Universe during inflation in the slow-roll approximation. Taking the
Starobinsky model as an example, we display exact solutions for the time
evolution of the scalar field $\phi(t)$, scale factor $a(t)$, Hubble function
$H(t)$, equation of state parameter $\omega(t)$ and acceleration of the scale
factor $\ddot{a}(t)$ among other quantities of interest.
