Exact solution of scalar field cosmology with exponential potentials and transient acceleration

TL;DR

This paper derives explicit solutions for scalar field cosmology with exponential potentials in any dimension, revealing conditions for eternal, transient, or no acceleration, and showing higher dimensions shorten acceleration periods.

Contribution

It provides a straightforward method to find exact solutions in scalar field cosmology with exponential potentials across dimensions, detailing acceleration behaviors.

Findings

Explicit solutions for scalar field cosmology in arbitrary dimensions.

Conditions for eternal, transient, or no acceleration identified.

Higher dimensions reduce the duration of accelerated expansion.

Abstract

We show that the general solution of scalar field cosmology in $d$ dimensions with exponential potentials for flat Robertson-Walker metric can be found in a straightforward way by introducing new variables which completely decouple the system. The explicit solution shows the region of parameters where the expansion has eternal acceleration, transient periods of acceleration, or no period of acceleration at all. In the cases of transient acceleration, the energy density exhibits a plateau during the accelerated expansion, where $p\cong -\rho$, due to dominance of potential energy. We determine the interval of accelerated expansion in terms of a simple formula. In particular, it shows that the period of accelerated expansion decreases in higher dimensions.