Accelerated Expansion of the Universe in a Higher Dimensional Modified Gravity with Euler-Poincar\'e Terms

TL;DR

This paper explores a higher-dimensional modified gravity theory incorporating Euler-Poincaré terms, demonstrating that such terms can lead to accelerated expansion of the external universe while internal dimensions contract, offering insights into cosmological evolution.

Contribution

It introduces a higher-dimensional gravity model with Euler-Poincaré terms and analyzes steady state solutions with accelerated external expansion and contracting internal space.

Findings

Euler-Poincaré terms are crucial for accelerated expansion.

Higher-dimensional steady state cosmologies with constant volume are possible.

External space expands while internal space contracts in these models.

Abstract

A higher dimensional modified gravity theory with an action that includes dimensionally continued Euler-Poincar\'e forms up to second order in curvatures is considered. The variational field equations are derived. Matter in the universe at large scales is modeled by a fluid satisfying an equation of state with dimensional dichotomy. We study solutions that describe higher dimensional steady state cosmologies with constant volume for which the three dimensional external space is expanding at an accelerated rate while the (compact) internal space is contracting. We showed that the second order Euler-Poincar\'e term in the constructions of higher dimensional steady state cosmologies could be crucial.