Isotropic evolution of a JBD anisotropic Bianchi universe

TL;DR

This paper investigates the early universe's isotropic evolution within Brans-Dicke scalar-tensor cosmology, showing that anisotropic Bianchi type VII models tend to isotropize and behave like standard cosmological models, with stability against anisotropic perturbations.

Contribution

It provides a detailed analysis of Bianchi type VII models in Jordan-Brans-Dicke theory, demonstrating isotropization and stability, and introduces the intrinsic time variable for better understanding of the evolution.

Findings

Bianchi-VII$_0$ model exhibits isotropic expansion similar to FRW spacetime.

Models with $h eq 0$ develop strong curvature singularities and collapse.

Universes isotropize from anisotropic initial conditions and are stable against perturbations.

Abstract

I study the dynamical effects due to the Brans-Dicke scalar $\phi$-field at the early stages of a supposedly anisotropic Universe expansion in the scalar-tensor cosmology of Jordan-Brans-Dicke. This is done considering the behaviour of the general solutions for the homogeneous model of Bianchi type VII in the vacuum case. I conclude that the Bianchi-VII$_0$ model shows an isotropic expansion and that its only physical solution is equivalent to a Friedman-Robertson-Walker spacetime whose evolution can, depending on the value of the JBD coupling constant, begin in a singularity and, after expanding (inflating, if $\omega>0$), shrink to another, or starting in a non-singular state, collapse to a singularity. I also conclude that the general Bianchi-VII$_h$ (with $h\neq 0$) models show strong curvature singularities producing a complete collapse of the homogeinity surfaces to 2D-manifolds, to 1D-manifolds or to single points. Our analysis depends crucially on the introduction of the so-called intrinsic time, $\Phi$, as the product of the JBD scalar field $\phi$ times a mean scale factor $a^3=a_1a_2a_3$, in which the finite-cosmological-time evolution of this universe unfolds into an infinite $\Phi$-range. These universes isotropize from an anisotropic initial state, thence I conclude that they are stable against anisotropic perturbations.