Wave-like Solutions for Bianchi type-I cosmologies in 5D

TL;DR

This paper derives the most general wave-like solutions to 5D vacuum Einstein equations with self-similarity, generating anisotropic Bianchi type-I cosmological models relevant for early universe anisotropies.

Contribution

It introduces the comprehensive class of wave-like solutions in 5D, extending previous work to include anisotropic Bianchi type-I models with self-similarity.

Findings

Derivation of general wave-like solutions in 5D vacuum Einstein equations.

Generation of anisotropic Bianchi type-I cosmologies from these solutions.

Extension of previous spherical symmetry studies to more general anisotropic models.

Abstract

We derive exact solutions to the vacuum Einstein field equations in 5D, under the assumption that (i) the line element in 5D possesses self-similar symmetry, in the classical understanding of Sedov, Taub and Zeldovich, and that (ii) the metric tensor is diagonal and independent of the coordinates for ordinary 3D space. These assumptions lead to three different types of self-similarity in 5D: homothetic, conformal and "wave-like". In this work we present the most general wave-like solutions to the 5D field equations. Using the standard technique based on Campbell's theorem, they generate a large number of anisotropic cosmological models of Bianchi type-I, which can be applied to our universe after the big-bang, when anisotropies could have played an important role. We present a complete review of all possible cases of self-similar anisotropic cosmologies in 5D. Our analysis extends a number of previous studies on wave-like solutions in 5D with spatial spherical symmetry.