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In this paper we have constructed a gauge-invariant extension of a generic Horava Gravity (HG) model (with quadratic curvature terms) in linearized version in a systematic procedure. No additional fields are introduced. The linearized HG model is explicitly shown to be a gauge fixed version of the Einstein Gravity (EG) thus proving the Bellorin–Restuccia conjecture in a robust way. In the process we have explicitly computed the correct Hamiltonian dynamics using Dirac Brackets appearing from the Second Class Constraints present in the HG model. We comment on applying this scheme to the full nonlinear HG.

With the goal of giving evidence for the theoretical consistency of the Hořava theory, we perform a Hamiltonian analysis on a classical model suitable for analyzing its effective dynamics at large distances. The model is the lowest-order truncation of the Hořava Theory with the detailed-balance condition. We consider the pure gravitational theory without matter sources. The model has the same potential term of general relativity, but the kinetic term is modified by the inclusion of an arbitrary coupling constant λ. Since this constant breaks the general covariance under spacetime diffeomorphisms, it is believed that arbitrary values of λ deviate the model from general relativity. We show that this model is not a deviation at all, instead it is completely equivalent to general relativity in a particular partial gauge fixing for it. In doing this, we clarify the role of a second-class constraint of the model.

We analyze the radiative and nonradiative linearized variables in a gravity theory within the family of the nonprojectable Hořava theories, the Hořava theory at the kinetic-conformal point. There is no extra mode in this formulation, the theory shares the same number of degrees of freedom with general relativity. The large-distance effective action, which is the one we consider, can be given in a generally-covariant form under asymptotically flat boundary conditions, the Einstein-aether theory under the condition of hypersurface orthogonality on the aether vector. In the linearized theory, we find that only the transverse-traceless tensorial modes obey a sourced wave equation, as in general relativity. The rest of variables are nonradiative. The result is gauge-independent at the level of the linearized theory. For the case of a weak source, we find that the leading mode in the far zone is exactly Einstein’s quadrupole formula of general relativity, if some coupling constants are properly identified. There are no monopoles nor dipoles in this formulation, in distinction to the nonprojectable Horava theory outside the kinetic-conformal point. We also discuss some constraints on the theory arising from the observational bounds on Lorentz-violating theories.

In this work, we elaborate on the finite action for wormholes in higher derivative theories as well as for wormholes. Both non-traversable and traversable wormholes in theories with higher curvature invariants posses finite action.

We study the evolution of scalar perturbations in inflationary epoch with a single Lifshitz scalar in the context of the BPSH theory, which generalizes the original non-projectable Horava Lifshitz gravity. We consistently solve the evolution of the coupled scalar graviton and the inflaton fluctuation and derive the isocurvature perturbation. We find that the isocurvature mode grows in high energy.

Horava-Lifshitz gravity has covariance only under the foliation-preserving diffeomorphism. This implies that the quantities on the constant-time hypersurfaces should be regular. In the original theory, the projectability condition which strongly restricts the lapse function is proposed. We assume that a star is filled with a perfect fluid, that it has the reflection symmetry about the equatorial plane. As a result, we find a no-go theorem for stationary axisymmetric star solutions in projectable Horava-Lifshitz gravity under the physically reasonable assumptions on the matter sector.