Cosmological scaling solutions of minimally coupled scalar fields in three dimensions

We examine Friedmann–Robertson–Walker models in three spacetime dimensions. The matter content of the models is composed of a perfect fluid, with a γ-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−2ν , where a denotes the scale factor. Cosmological solutions are presented for different range of values of γ and ν. The potential required to agree with the above red-shift for the scalar field energy density is also calculated. During the last years a great number of works have been dedicated to study three-dimensional gravity, particularly after it was shown to be a soluble system [1] and to contain black hole solutions [2]-[3]. However, previously to this results, cosmological models were considered in three-dimensional gravity. In particular, some Friedmann–Robertson–Walker (FRW) models were analyzed in [4, 5, 6]. Recently, the cosmic holographic principle has