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Concept# Hořava–Lifshitz gravity

Résumé

Hořava–Lifshitz gravity (or Hořava gravity) is a theory of quantum gravity proposed by Petr Hořava in 2009. It solves the problem of different concepts of time in quantum field theory and general relativity by treating the quantum concept as the more fundamental so that space and time are not equivalent (anisotropic) at high energy level. The relativistic concept of time with its Lorentz invariance emerges at large distances. The theory relies on the theory of foliations to produce its causal structure. It is related to topologically massive gravity and the Cotton tensor. It is a possible UV completion of general relativity. Also, the speed of light goes to infinity at high energies. The novelty of this approach, compared to previous approaches to quantum gravity such as Loop quantum gravity, is that it uses concepts from condensed matter physics such as quantum critical phenomena. Hořava's initial formulation was found to have side-effects such as predicting very different results for a spherical Sun compared to a slightly non-spherical Sun, so others have modified the theory. Inconsistencies remain, though progress was made on the theory. Nevertheless, observations of gravitational waves emitted by the neutron-star merger GW170817 contravene predictions made by this model of gravity. Some have revised the theory to account for this.
Hořava originally imposed the theory to satisfy the detailed balance condition which considerably reduces the number of terms in the action.

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Publications associées (7)

Personnes associées (2)

Unités associées (1)

Sergey Sibiryakov, Diego Blas Temino, Mario Herrero Valea

We compute the beta functions of marginal couplings in projectable Horava gravity in 2 + 1 spacetime dimensions. We show that the renormalization group flow has an asymptotically free fixed point in the ultraviolet (UV), establishing the theory as a UV-complete model with dynamical gravitational degrees of freedom. Therefore, this theory may serve as a toy model to study fundamental aspects of quantum gravity. Our results represent a step forward towards understanding the UV properties of realistic versions of Horava gravity.

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We prove perturbative renormalizability of projectable Horava gravity. The key element of the argument is the choice of a gauge which ensures the correct anisotropic scaling of the propagators and their uniform falloff at large frequencies and momenta. This guarantees that the counterterms required to absorb the loop divergences are local and marginal or relevant with respect to the anisotropic scaling. Gauge invariance of the counterterms is achieved by making use of the background-covariant formalism. We also comment on the difficulties of this approach when addressing the renormalizability of the nonprojectable model.

Hillary Sanctuary, Diego Blas Temino

We study the radiation of gravitational waves by self-gravitating binary systems in the low-energy limit of Horava gravity. We find that the predictions for the energy-loss formula of general relativity are modified already for Newtonian sources: the quadrupole contribution is altered, in part due to the different speed of propagation of the tensor modes; furthermore, there is a monopole contribution stemming from an extra scalar degree of freedom. A dipole contribution only appears at higher post-Newtonian order. We use these findings to constrain the low-energy action of Horava gravity by comparing them with the radiation damping observed for binary pulsars. Even if this comparison is not completely appropriate-since compact objects cannot be described within the post-Newtonian approximation-it represents an order of magnitude estimate. In the limit where the post-Newtonian metric coincides with that of general relativity, our energy-loss formula provides the strongest constraints for Horava gravity at low-energies.

2011