Application of the Abel equation of the 1st kind to inflation analysis of non-exactly solvable cosmological models

Artyom V. Yurov, Anna V. Yaparova, Valerian A. Yurov1

Abstract

We revisit the relationship between the Einstein-Friedmann and Abel equations to demonstrate how the latter might be applied to the inflationary analysis in a spatially-flat Friedmann universe filled with a real-valued scalar field. The analysis is performed for three distinct cases of polynomial potentials. As a result of numerical integration of the Abel equation, necessary and sufficient conditions for both slow rolling and inflation are estimated with respect to the initial value of the field. In addition, the relationship between the slow-rolling condition and the inflation is ascertained.

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