(An)Isotropic models in scalar and scalar-tensor cosmologies

TL;DR

This paper investigates how the gravitational constant and cosmological constant vary over time in different scalar and scalar-tensor cosmological models, finding solutions that are isotropic, noninflationary, with a decreasing cosmological constant and increasing gravitational constant.

Contribution

It provides exact power-law solutions in generalized geometries under self-similarity, comparing various models to understand the behavior of fundamental constants in cosmology.

Findings

Solutions are isotropic and noninflationary.

The cosmological constant decreases over time.

The gravitational constant increases over time.

Abstract

We study how the constants $G$ and $\Lambda$ may vary in different theoretical models (general relativity with a perfect fluid, scalar cosmological models (\textquotedblleft quintessence\textquotedblright) with and without interacting scalar and matter fields and a scalar-tensor model with a dynamical $\Lambda$) in order to explain some observational results. We apply the program outlined in section II to study three different geometries which generalize the FRW ones, which are Bianchi \textrm{V}, \textrm{VII}$_{0}$ and \textrm{IX}, under the self-similarity hypothesis. We put special emphasis on calculating exact power-law solutions which allow us to compare the different models. In all the studied cases we arrive to the conclusion that the solutions are isotropic and noninflationary while the cosmological constant behaves as a positive decreasing time function (in agreement with the current observations) and the gravitational constant behaves as a growing time function.