Isotropization of Bianchi-Type Cosmological Solutions in Brans-Dicke Theory

TL;DR

This paper explores how anisotropic Bianchi-type cosmological solutions in Brans-Dicke theory can evolve towards isotropy over time, identifying conditions under which solutions become stable and isotropic.

Contribution

It introduces a reduction method showing that a broad class of solutions, including anisotropic models, can be analyzed for isotropization in Brans-Dicke cosmology.

Findings

Existence of a class of solutions that can isotropize over time.

Reduction procedure for analyzing anisotropic solutions.

Potential stability of isotropic solutions under perturbations.

Abstract

The cosmic, general analitic solutions of the Brans--Dicke Theory for the flat space of homogeneous and isotropic models containing perfect, barotropic, fluids are seen to belong to a wider class of solutions --which includes cosmological models with the open and the closed spaces of the Friedmann--Robertson--Walker metric, as well as solutions for models with homogeneous but anisotropic spaces corresponding to the Bianchi--Type metric clasification-- when all these solutions are expressed in terms of reduced variables. The existence of such a class lies in the fact that the scalar field, $\phi$, times a function of the mean scale factor or ``volume element'', $a^3 = a_1 a_2 a_3$, which depends on time and on the barotropic index of the equation of state used, can be written as a function of a ``cosmic time'' reduced in terms of another function of the mean scale factor depending itself again on the barotropic index but independent of the metrics here employed. This reduction procedure permites one to analyze if explicitly given anisotropic cosmological solutions ``isotropize'' in the course of their time evolution. For if so can happen, it could be claimed that there exists a subclass of solutions that is stable under anisotropic perturbations.