Non-variational scalar field cosmology: Exact Bianchi I solutions for near-minimal scalar fields

TL;DR

This paper derives four exact Bianchi I cosmological solutions with near-minimal scalar fields, revealing diverse phenomena like singularities and oscillations, and analyzes their stability against inhomogeneous perturbations.

Contribution

It introduces new exact solutions for non-variational scalar field cosmology and examines their stability, expanding understanding of possible cosmic evolutions.

Findings

Solutions exhibit Big Bang, Big Crunch, Big Rip, and cyclic behaviors.

Oscillatory solutions are unstable to inhomogeneous perturbations.

Solutions with Big Rip singularity are stable to perturbations.

Abstract

The purpose of this work is to investigate spatially homogeneous and flat cosmological solutions of the Einstein equations coupled to a non-variational ``near-minimal'' scalar field. This coupling model represents a minimal departure from standard theory by decoupling the scalar field's self-interaction term from the derivative of its potential. By assuming a quadratic potential and a self-interaction term that is proportional to the potential, we derive four new exact Bianchi I solutions. We demonstrate that these solutions produce a diverse range of cosmological phenomena, including Big Bang, Big Crunch, and Big Rip singularities, as well as oscillatory (``cyclic'') behaviour. For our exact solutions, these singularities occur in infinite proper time and hence are never truly reachable by an observer. To assess the stability of these cosmologies, we perform a numerical stability analysis against spatially inhomogeneous perturbations of the mean curvature. We find that the oscillatory solution is unstable to perturbations of this type, as are solutions in possession of a crushing singularity. Conversely, solutions with a Big Rip singularity (at infinity) are stable to spatially inhomogeneous perturbations of the mean curvature.