Quantizing Horava-Lifshitz Gravity via Causal Dynamical Triangulations

TL;DR

This paper extends causal dynamical triangulations to include curvature squared terms, exploring phase structures and their relation to classical Horava-Lifshitz gravity solutions through Monte Carlo simulations.

Contribution

It introduces a discrete version of curvature squared terms into CDT and investigates the resulting spacetime phases and their classical gravity correspondence.

Findings

Identification of known and new macroscopic spacetime phases

Evidence of phase transition between de Sitter-like and static phases

Preliminary support for classical Horava-Lifshitz gravity solutions

Abstract

We extend the discrete Regge action of causal dynamical triangulations to include discrete versions of the curvature squared terms appearing in the continuum action of (2+1)-dimensional projectable Horava-Lifshitz gravity. Focusing on an ensemble of spacetimes whose spacelike hypersurfaces are 2-spheres, we employ Markov chain Monte Carlo simulations to study the path integral defined by this extended discrete action. We demonstrate the existence of known and novel macroscopic phases of spacetime geometry, and we present preliminary evidence for the consistency of these phases with solutions to the equations of motion of classical Horava-Lifshitz gravity. Apparently, the phase diagram contains a phase transition between a time-dependent de Sitter-like phase and a time-independent phase. We speculate that this phase transition may be understood in terms of deconfinement of the global gravitational Hamiltonian integrated over a spatial 2-sphere.