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

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 $p\cong -ρ$, 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.