Algebraic expansions for curvature coupled scalar field models

TL;DR

This paper develops algebraic power series expansions to analyze the late-time behavior of curvature coupled scalar field models in cosmology, providing a formal framework for understanding their asymptotics.

Contribution

It introduces algebraic analogues of Einstein scalar field equations and constructs unique formal solutions for models with accelerated expansion.

Findings

Solutions are consistent with known asymptotic behaviors.

Provides a method to predict large-time dynamics of scalar field cosmologies.

Formal solutions are inductively constructed and shown to be unique.

Abstract

A late time asymptotic perturbative analysis of curvature coupled complex scalar field models with accelerated cosmological expansion is carried out on the level of formal power series expansions. For this, algebraic analogues of the Einstein scalar field equations in Gaussian coordinates for space-time dimensions greater than two are postulated and formal solutions are constructed inductively and shown to be unique. The results obtained this way are found to be consistent with already known facts on the asymptotics of such models. In addition, the algebraic expansions are used to provide a prospect of the large time behaviour that might be expected of the considered models.