# Anisotropic evolution of D-dimensional FRW spacetime

## TL;DR

This paper derives exact solutions for the evolution of higher-dimensional FRW cosmologies with anisotropic scale factors, revealing regimes that mimic standard cosmology and can explain early and late accelerated expansion.

## Contribution

It provides the first exact solutions for D-dimensional anisotropic FRW spacetimes with a single fluid, connecting early universe inflation and late-time acceleration within a higher-dimensional framework.

## Key findings

- Exact solutions for D-dimensional anisotropic FRW equations.
- Identification of regimes mimicking 4D cosmology and accelerated expansion.
- Transition timescales compatible with early universe epochs.

## Abstract

We examine the time evolution of the D=d+4 dimensional Einstein field equations subjected to a flat Robertson-Walker metric where the 3D and higher-dimensional scale factors are allowed to evolve at different rates. We find the exact solution to these equations for a single fluid component, which yields two limiting regimes offering the 3D scale factor as a function of the time. The fluid regime solution closely mimics that described by 4D FRW cosmology, offering a late-time behavior for the 3D scale factor after becoming valid in the early universe, and can give rise to a late-time accelerated expansion driven by vacuum energy. This is shown to be preceded by an earlier volume regime solution, which offers a very early-time epoch of accelerated expansion for a radiation-dominated universe for d=1. The time scales describing these phenomena, including the transition from volume to fluid regime, are shown to fall within a small fraction of the first second when the fundamental constants of the theory are aligned with the Planck time. This model potentially offers a higher-dimensional alternative to scalar-field inflationary theory and a consistent cosmological theory, yielding a unified description of early- and late-time accelerated expansions via a 5D spacetime scenario.