The Behavior of Kasner Cosmologies with Induced Matter

TL;DR

This paper explores anisotropic Bianchi type-I cosmologies within a 5D induced matter framework, deriving solutions and analyzing the long-term behavior of the universe's expansion and the fifth dimension.

Contribution

It generalizes the induced matter model to anisotropic Bianchi type-I cosmologies and derives new solutions for the 5D Einstein equations with induced matter.

Findings

Positive density leads to contraction of the fifth dimension over time.

Derived explicit solutions for 5D Einstein equations with anisotropic geometry.

Analyzed the impact of induced matter on cosmological dynamics.

Abstract

We extend the induced matter model, previously applied to a variety of isotropic cases, to a generalization of Bianchi type-I anisotropic cosmologies. The induced matter model is a 5D Kaluza-Klein approach in which assumptions of compactness are relaxed for the fifth coordinate, leading to extra geometric terms. One interpretation of these extra terms is to identify them as an ``induced matter'' contribution to the stress-energy tensor. In similar spirit, we construct a five dimensional metric in which the spatial slices possess Bianchi type-I geometry. We find a set of solutions for the five dimensional Einstein equations, and determine the pressure and density of induced matter. We comment on the long-term dynamics of the model, showing that the assumption of positive density leads to the contraction over time of the fifth scale factor.