Late Time Acceleration of the 3-Space in a Higher Dimensional Steady State Universe in Dilaton Gravity

TL;DR

This paper explores higher-dimensional cosmological models in dilaton gravity, showing how internal dimensions influence late-time acceleration and potential Big Rip scenarios, with exact solutions for specific dilaton couplings.

Contribution

It provides new solutions for (1+3+n)-dimensional steady state universes with dilaton fields, analyzing conditions for accelerated expansion compatible with observations.

Findings

3-space can transition from deceleration to acceleration

All models end with a Big Rip in finite time

Exact solutions are derived for specific dilaton couplings w=1 and w=1/2

Abstract

We present cosmological solutions for (1+3+n)-dimensional steady state universe in dilaton gravity with an arbitrary dilaton coupling constant w and exponential dilaton self-interaction potentials in the string frame. We focus particularly on the class in which the 3-space expands with a time varying deceleration parameter. We discuss the number of the internal dimensions and the value of the dilaton coupling constant to determine the cases that are consistent with the observed universe and the primordial nucleosynthesis. The 3-space starts with a decelerated expansion rate and evolves into accelerated expansion phase subject to the values of w and n, but ends with a Big Rip in all cases. We discuss the cosmological evolution in further detail for the cases w=1 and w=1/2 that permit exact solutions. We also comment on how the universe would be conceived by an observer in four dimensions who is unaware of the internal dimensions and thinks that the conventional general relativity is valid at cosmological scales.