Evolution of the universe during the inflationary epoch

TL;DR

This paper provides detailed solutions for the evolution of the universe during the inflationary epoch using the Starobinsky model, focusing on the slow-roll approximation and key cosmological parameters.

Contribution

It offers exact solutions for inflationary dynamics in the Starobinsky model, filling a gap in analytical solutions during this epoch.

Findings

Exact solutions for scalar field and scale factor evolution.

Analysis of the Hubble function and equation of state during inflation.

Insights into the acceleration of the universe in the inflationary era.

Abstract

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.