Anistropic Invariant FRW Cosmology

TL;DR

This paper explores an anisotropic scaling invariant cosmological model, leading to a Schrödinger-like quantum equation and suggesting conditions under which the big bang singularity may be avoided.

Contribution

It introduces anisotropic scaling invariance into the FRW cosmology framework, resulting in a Schrödinger-type quantization and potential singularity avoidance.

Findings

Quantization yields a Schrödinger-like equation.

Numerical solutions support singularity avoidance.

Model modifies traditional cosmological dynamics.

Abstract

In this paper we study the effects of including anisotropic scaling invariance in the minisuperspace Lagrangian for a universe modelled by the Friedman-Robertson-Walker metric, a massless scalar field and cosmological constant. We find that canonical quantization of this system leads to a Schroedinger type equation, thus avoiding the frozen time problem of the usual Wheeler-DeWitt equation. Furthermore, we find numerical solutions for the classical equations of motion, and we also find evidence that under some conditions the big bang singularity is avoided in this model.