1302.6017 (Anna V. Yaparova et al.)

Application of the Abel Equation of the 1st kind to an inflation
analysis of non-exactly solvable cosmological models    [PDF]

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

In this paper we revisit the relationship between the Einstein--Friedman and the Abel equations to demonstrate how it might be applied to the inflationary analysis in a flat Friedman universe filled with a real-valued scalar field. The analysis is performed for three distinct cases of polynomial potentials. As a result of a numeric integration of Abel equation, the necessary and sufficient conditions for both slow-rolling and inflation proper 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.

View original: http://arxiv.org/abs/1302.6017