Cosmological scaling solutions of minimally coupled scalar fields in three dimensions

Abstract

We examine Friedmann-Robertson-Walker models in three spacetime dimensions. The matter content of the models is composed of a perfect fluid, with a $\gamma$-law equation of state, and a homogeneous scalar field minimally coupled to gravity with a self-interacting potential whose energy density red-shifts as $a^{-2 \nu}$, where a denotes the scale factor. Cosmological solutions are presented for different range of values of $\gamma$ and $\nu$. The potential required to agree with the above red-shift for the scalar field energy density is also calculated.