Inflation for Bianchi IX model

TL;DR

This paper investigates how inflation can reduce initial anisotropy in the early universe modeled by Bianchi IX, identifying conditions that lead to negligible anisotropy despite complex Einstein equations.

Contribution

It demonstrates that a wide range of initial conditions in the Bianchi IX model can result in inflationary periods that diminish anisotropy, extending understanding beyond isotropic models.

Findings

Inflation can significantly reduce anisotropy in Bianchi IX universe.

A large set of initial conditions leads to negligible anisotropy after inflation.

Non-linearity of Einstein's equations makes finding these conditions non-trivial.

Abstract

The influence of Inflation on initial (i.e. at Planck's epoch) large anisotropy of the Universe is studied, considering a more general metric than the isotropic one: the locally rotationally symmetric (L.R.S.) Bianchi IX metric. We find, then, a large set of initial conditions of intrinsic curvature and shear allowing an inflationary epoch that make the anisotropy negligible. These are not trivial because of the non-linearity of the Einstein's equations.