  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.
