We present the interesting case of the 2+1 nonprojectable Horava theory formulated at the critical point, where it does not posses local degrees of freedom. The critical point is defined by the value of a coupling constant of the theory. We discuss how, in spite of the absence of degrees of freedom, the theory admits solutions with nonflat or nonconstant curvature. We consider the theory without cosmological constant and without terms of higher order derivatives, hence this is an effect that can be seen at the same order of 2+1 general relativity. We present an exact nonflat solution that is not asymptotically flat. The presence of solutions with nontrivial curvature seems to be related to the relaxing of the asymptotically flat condition. We discuss that there is no analogue of Newtonian potential in this theory, and a broad class of asymptotically flat geometries leads to the restriction that the only solutions that can be found among them are the flat ones.
We show that in the Hořava-Lifshitz theory at the kinetic-conformal point, in the low energy regime, a wave zone for asymptotically flat fields can be consistently defined. In it, the physical degrees of freedom, the transverse traceless tensorial modes, satisfy a linear wave equation. The Newtonian contributions, among which there are terms which manifestly break the relativistic invariance, are non-trivial but do not obstruct the free propagation (radiation) of the physical degrees of freedom. For an appropriate value of the couplings of the theory, the wave equation becomes the relativistic…
We discuss a new covariant scalar-tensor system aimed to realise Hořava proposal for a power-counting renormalizable theory of gravity, with the special feature of not propagating scalar degrees of freedom in an appropriate gauge. The theory is characterized by a new symmetry acting on the metric, that can protect the particular form of its interactions. The set-up spontaneously breaks Lorentz symmetry by means of a time-like scalar field profile. By selecting a unitary gauge for the scalar, we show that this theory describes the dynamics of a spin two degree of freedom, whose equations of mot…
We consider the Hamiltonian formulation of Horava gravity in arbitrary dimensions, which has been proposed as a renormalizable gravity model for quantum gravity without the ghost problem. We study the "full" constraint analysis of the "non-projectable" Horava gravity whose potential, V(R), is an arbitrary function of the (intrinsic) Ricci scalar R. We find that there exist generally distinct cases of this theory, depending on (i) whether the Hamiltonian constraint generates new (second-class) constraints (Cases A, C) or just fixes the associated Lagrange multipliers (Case B), or (ii) whether t…
Asymptotically free mimetic gravity has been introduced as a proposal for a classical limiting curvature theory with the purpose of singularity resolution. It was found that in a spatially flat universe an initial stage of exponential expansion with graceful exit is a generic consequence, regardless of the matter content. In this work I will analyze linear stability of cosmological perturbations in such a model, considering only the degrees of freedom of pure mimetic gravity. I show that the addition of Hořava-gravity-like higher order spatial curvature terms can lift the gradient instability …
The gravitational waves of Hořava gravity, their polarization states and their possible observational signatures are discussed. Using the gauge-invariant variable formalism, we found the three polarization modes in Hořava gravity excited by the three physical degrees of freedom contained in this theory. In particular, the scalar degree of freedom excites a mix of the transverse breathing and the longitudinal polarizations. The constraints from the previous experimental observations are taken into account, especially including the speed bound from the observations of GW170817 and GRB 170817A. I…
The Horava theory in 2+1 dimensions can be formulated at a critical point in the space of coupling constants where it has no local degrees of freedom. This suggests that this critical case could share many features with 2+1 general relativity, in particular its large-distance effective action that is of second order in derivatives. To deepen on this relationship, we study the asymptotically flat solutions of the effective action. We take the general definition of asymptotic flatness from 2+1 general relativity, where an asymptotically flat region with a nonfixed conical angle is approached. We…
Using the qualitative theory of differential equations, the global dynamics of a cosmological model based on Horava-Lifshitz gravity is studied in the space with zero curvature in the presence of the non-zero cosmological constant.
I revisit rotating black hole solutions in three-dimensional Horava gravity with z = 2 as a simpler set-up of the renormalizable quantum gravity `a la Lifshitz and DeWitt. The solutions have a curvature singularity at the origin for a non-vanishing rotation parameter J, unlike the black holes in three-dimensional Einstein gravity. For anti-de Sitter space, there are black hole event horizons as usual and the singularity is not naked, in agreement with the cosmic censorship. On the other hand, for flat or de Sitter space, the earlier solution has also a cosmic-censorship problem because there a…
We contrast the dynamics of the Horava theory with anisotropic Weyl symmetry with the case when this symmetry is explicitly broken, which is called the kinetic-conformal Horava theory. To do so we perform the canonical formulation of the anisotropic conformal theory at the classical level with a general conformal potential. Both theories have the generator of the anisotropic Weyl transformations as a constraint but it changes from first to second-class when the Weyl symmetry is broken. The FDiff-covariant vector a_i = \partial_i \ln N plays the role of gauge connection for the anisotropic Weyl…
Within the general framework of spatially covariant theories of gravity, we study the conditions for having only the two tensorial degrees of freedom. Generally, there are three degrees of freedom propagating in the theory, of which two are tensorial and one is of the scalar type. Through a detailed Hamiltonian analysis, we find two necessary and sufficient conditions to evade the scalar type degree of freedom. The first condition implies that the lapse-extrinsic curvature sector must be degenerate. The second condition ensures that the dimension of the phase space at each spacetime point is e…
The cuscuton was introduced in the context of cosmology as a field with infinite speed of propagation. It has been claimed to resemble Hořava gravity in a certain limit, and it is a good candidate for an ether theory in which a time-dependent cosmological constant appears naturally. The analysis of its properties is usually performed in the Lagrangian framework, which makes issues like the counting of its dynamical degrees of freedom less clear-cut. Here we perform a Hamiltonian analysis of the theory. We show that the homogeneous limit with local degrees of freedom has singular behavior in th…
Most existing theories of dark energy and/or modified gravity, involving a scalar degree of freedom, can be conveniently described within the framework of the Effective Theory of Dark Energy, based on the unitary gauge where the scalar field is uniform. We extend this effective approach by allowing the Lagrangian in unitary gauge to depend on the time derivative of the lapse function. Although this dependence generically signals the presence of an extra scalar degree of freedom, theories that contain only one propagating scalar degree of freedom, in addition to the usual tensor modes, can be c…
We perform a rigorous piecewise-flat discretization of classical general relativity in the first-order formulation, in both 2+1 and 3+1 dimensions, carefully keeping track of curvature and torsion via holonomies. We show that the resulting phase space is precisely that of spin networks, the quantum states of discrete spacetime in loop quantum gravity, with additional degrees of freedom called edge modes, which control the gluing between cells. This work establishes, for the first time, a rigorous proof of the equivalence between spin networks and piecewise-flat geometries with curvature and to…
We make a perturbative analysis of spatially covariant gravity only respecting spatial symmetries, of which the Lagrangian includes the dynamic lapse function and the coupling term of spatial curvature and extrinsic curvature. We show that the theory propagates 2 scalar degrees of freedom, as long as the kinetic terms are degenerate, it propagates a single scalar mode at the linear order. Then we calculate the scalar and tensor power spectra. Finally, we study cosmological perturbations in mimetic gravity in the presence of spatially covariant gravity. The original spatially covariant theory p…
We analyze the model of a self-interacting $ϕ^4_{\star}$ scalar field theory in Snyder-de Sitter space. After analytically computing the one-loop beta functions {in the small noncommutativity and curvature limit}, we solve numerically the corresponding system of differential equations, showing that in this limit the model possesses at least one regime in which the theory is asymptotically free. Moreover, in a given region of the parameter space we also observe a peculiar running of the parameter associated to the curvature, which changes its sign and therefore can be interpreted as a transitio…
