Phenomenologically Viable Lorentz-Violating Quantum Gravity

Horcava's Lifschitz point gravity has many desirable features, but in its original incarnation one is forced to accept a nonzero cosmological constant of the wrong sign to be compatible with observation. We develop an extension of Horcava's model that abandons detailed balance and regains parity invariance, and in 3+1 dimensions exhibit all five marginal (renormalizable) and four relevant (super-renormalizable) operators, as determined by power counting. We also consider the classical limit of this theory, evaluate the Hamiltonian and supermomentum constraints, and extract the classical equations of motion in a form similar to the Arnowitt-Deser-Misner formulation of general relativity. This puts the model in a framework amenable to developing detailed precision tests.