Cosmological scaling solutions of minimally coupled scalar fields in three dimensions

TL;DR

This paper explores cosmological models in three dimensions with scalar fields and perfect fluids, deriving solutions and potentials that match specific energy density red-shifts, enhancing understanding of lower-dimensional cosmology.

Contribution

It provides new exact solutions for 3D cosmological models with scalar fields and calculates the potentials needed for specific energy density behaviors.

Findings

Derived cosmological solutions for different parameters.

Calculated scalar field potentials matching energy density red-shifts.

Enhanced understanding of 3D cosmological dynamics.

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.