Scalar field in cosmology: Potential for isotropization and inflation

TL;DR

This paper investigates scalar field potentials that can cause isotropization and inflation in cosmological models, solving direct and inverse problems to identify conditions for these phenomena in Bianchi type-I and isotropic space-times.

Contribution

It derives the general form of scalar field potentials that lead to isotropization and inflation, addressing both direct and inverse problems in cosmological models.

Findings

Identified potentials that induce isotropization in anisotropic models.

Found potentials that support inflationary regimes in isotropic space.

Solved both direct and inverse problems for scalar field potentials.

Abstract

The important role of scalar field in cosmology was noticed by a number of authors. Due to the fact that the scalar field possesses zero spin, it was basically considered in isotropic cosmological models. If considered in an anisotropic model, the linear scalar field does not lead to isotropization of expansion process. One needs to introduce scalar field with nonlinear potential for the isotropization process to take place. In this paper the general form of scalar field potentials leading to the asymptotic isotropization in case of Bianchi type-I cosmological model, and inflationary regime in case of isotropic space-time is obtained. In doing so we solved both direct and inverse problem, where by direct problem we mean to find metric functions and scalar field for the given potential, whereas, the inverse problem means to find the potential and scalar field for the given metric function. The scalar field potentials leading to the inflation and isotropization were found both for harmonic and proper synchronic time.