Generalized power expansions in cosmology

TL;DR

This paper presents an algorithm for deriving generalized power asymptotic expansions of solutions to Einstein equations in homogeneous cosmological models, aiding the analysis of their behavior near singularities or at large times.

Contribution

It introduces a novel algorithm for obtaining generalized power expansions of Einstein solutions, implemented in Maple V, with detailed calculations for specific equations.

Findings

Algorithm successfully derives asymptotic expansions near singularities.

Implementation in Maple V facilitates practical computations.

Provides insights into the behavior of cosmological models at extreme conditions.

Abstract

It is given an algorithm to obtain generalized power asymptotic expansions of the solutions of the Einstein equations arising for several homogeneous cosmological models. This allows to investigate their behavior near the initial singularity or for large times. An implementation of this algorithm in the CAS system Maple V Release 4 is described and detailed calculations for three equations are shown.