Classical and Quantum Bianchi Type III vacuum Horava - Lifshitz Cosmology

TL;DR

This paper explores classical and quantum solutions of Bianchi Type III vacuum cosmology within Horava-Lifshitz gravity, revealing singularities and specific quantum wave-functions for certain parameter values.

Contribution

It provides explicit classical solutions and quantum wave-functions for Bianchi Type III cosmology in Horava-Lifshitz gravity, including cases with Euclidean, Lorentzian, and neutral signatures.

Findings

Solutions develop curvature singularities as parameters approach Einsteinian values.

Explicit Wheeler-DeWitt solutions are obtained for specific parameters.

Wave-functions diverge in the Einsteinian limit.

Abstract

A diagonal Bianchi Type III space-time is treated, both at the classical and quantum level, in the context of Horava - Lifshitz gravity. The system of the classical equations of motion is reduced to one independent Abel's equation of the first kind. Closed form solution are presented for various values of the coupling constants appearing in the action. Due to the method used, solutions of Euclidean, Lorentzian and neutral signature are attained. The solutions corresponding to \lamda <> 1 are seen to develop curvature singularities as the other constants approach their Einsteinian values, in contrast to those with \lamda = 1 which tend to the known Einstein gravity solutions. At the quantum level, the resulting Wheeler-DeWitt equation is explicitly solved for \lamda = 1, \sigma = 0 and \lamda = 1/3 . The ensuing wave-functions diverge in the Einsteinian limit.