Cosmology in nonrelativistic general covariant theory of gravity

TL;DR

This paper explores a modified gravity theory proposed by Horava and Melby-Thompson, deriving its equations, applying it to cosmology, and analyzing perturbations, revealing potential for bouncing universe models and consistent gravitational wave modes.

Contribution

The paper derives the Hamiltonian, constraints, and cosmological equations in the new U(1) invariant Horava-Lifshitz gravity theory, extending previous work to include matter and perturbations.

Findings

Modified Friedmann equations with dark radiation and stiff-fluid terms.

Existence of bouncing universe solutions under certain conditions.

Scalar and vector perturbations vanish in Minkowski background, leaving only massless gravitons.

Abstract

Horava and Melby-Thompson recently proposed a new version of the Horava-Lifshitz theory of gravity, in which the spin-0 graviton is eliminated by introducing a Newtonian pre-potential $\phi$ and a local U(1) gauge field $A$. In this paper, we first derive the corresponding Hamiltonian, super-momentum constraints, the dynamical equations, and the equations for $\phi$ and $A$, in the presence of matter fields. Then, we apply the theory to cosmology, and obtain the modified Friedmann equation and the conservation law of energy, in addition to the equations for $\phi$ and $A$. When the spatial curvature is different from zero, terms behaving like dark radiation and stiff-fluid exist, from which, among other possibilities, bouncing universe can be constructed. We also study linear perturbations of the FRW universe with any given spatial curvature $k$, and derive the most general formulas for scalar perturbations. The vector and tensor perturbations are the same as those recently given by one of the present authors [A. Wang, Phys. Rev. D{\bf 82}, 124063 (2010)] in the setup of Sotiriou, Visser and Weinfurtner. Applying these formulas to the Minkowski background, we have shown explicitly that the scalar and vector perturbations of the metric indeed vanish, and the only remaining modes are the massless spin-2 gravitons.