Scalar field cosmology in three-dimensions

TL;DR

This paper presents an analytical solution to Einstein's equations in 2+1 dimensions with a scalar field, describing different cosmological models including flat, big bang with negative curvature, and models with horizons.

Contribution

It provides a new exact solution to 2+1-dimensional Einstein's equations with a scalar field, illustrating diverse cosmological scenarios.

Findings

Identifies three distinct space-times based on parameter values.

Describes models with flat space-time, big bang with negative curvature, and horizons.

Shows scalar field behavior transitions from real to imaginary.

Abstract

We study an analytical solution to the Einstein's equations in 2+1-dimensions. The space-time is dynamical and has a line symmetry. The matter content is a minimally coupled, massless, scalar field. Depending on the value of certain parameters, this solution represents three distinct space-times. The first one is flat space-time. Then, we have a big bang model with a negative curvature scalar and a real scalar field. The last case is a big bang model with event horizons where the curvature scalar vanishes and the scalar field changes from real to purely imaginary.