An exact solution of the five-dimensional Einstein equations with four-dimensional de Sitter-like expansion

TL;DR

This paper provides an exact five-dimensional Einstein solution that appears flat in five dimensions but models a four-dimensional early universe with de Sitter-like expansion, offering insights into higher-dimensional cosmology.

Contribution

It introduces a novel exact solution to five-dimensional Einstein equations that models early universe expansion in four dimensions.

Findings

The solution is Ricci and Riemann flat in five dimensions.

In four dimensions, it resembles a vacuum-dominated, de Sitter-like universe.

Provides a new mathematical framework for higher-dimensional cosmological models.

Abstract

We present an exact solution to the Einstein field equations which is Ricci and Riemann flat in five dimensions, but in four dimensions is a good model for the early vacuum-dominated universe.