Cosmology of the Lifshitz universe

TL;DR

This work extends Hořava-Lifshitz gravity to include a Lifshitz scalar under separate detailed balance and analyzes the resulting cosmology. It finds non-singular bouncing solutions and Euclidean vacua that qualitatively match CDT/QEG expectations in vacuum regimes, while inflation driven by the Lifshitz scalar on a classical background generally fails to produce a scale-invariant spectrum under the detailed-balance assumption, due to UV $k^6$ dispersion corrections. Relaxing the detailed-balance condition or modifying the scalar sector is proposed as a route to restore scale invariance, underscoring the interplay between UV completion and observable cosmology. The results illuminate how Horava gravity can mimic features of other quantum gravity approaches yet require careful treatment of perturbations to yield viable early-universe predictions.

Abstract

We study the ultraviolet complete non-relativistic theory recently proposed by Horava. After introducing a Lifshitz scalar for a general background, we analyze the cosmology of the model in Lorentzian and Euclidean signature. Vacuum solutions are found and it is argued the existence of non-singular bouncing profiles. We find a general qualitative agreement with both the picture of Causal Dynamical Triangulations and Quantum Einstein Gravity. However, inflation driven by a Lifshitz scalar field on a classical background might not produce a scale-invariant spectrum when the principle of detailed balance is assumed.