Comment on `Strong coupling in extended Horava-Lifshitz gravity'

We show that, contrary to the claim made in arXiv:0911.1299, the extended Horava gravity model proposed in arXiv:0909.3525 does not suffer from a strong coupling problem. By studying the observational constraints on the model we determine the bounds on the scale of the ultraviolet modification for which the proposal yields a phenomenologically viable, renormalizable and weakly coupled model of quantum gravity.Comment: A footnote discussing the absence of fine-tuning is adde

Cosmological constraints on Lorentz violating dark energy

The role of Lorentz invariance as a fundamental symmetry of nature has been lately reconsidered in different approaches to quantum gravity. It is thus natural to study whether other puzzles of physics may be solved within these proposals. This may be the case for the cosmological constant problem. Indeed, it has been shown that breaking Lorentz invariance provides Lagrangians that can drive the current acceleration of the universe without experiencing large corrections from ultraviolet physics. In this work, we focus on the simplest model of this type, called ThetaCDM, and study its cosmological implications in detail. At the background level, this model cannot be distinguished from LambdaCDM. The differences appear at the level of perturbations. We show that in ThetaCDM, the spectrum of CMB anisotropies and matter fluctuations may be affected by a rescaling of the gravitational constant in the Poisson equation, by the presence of extra contributions to the anisotropic stress, and finally by the existence of extra clustering degrees of freedom. To explore these modifications accurately, we modify the Boltzmann code CLASS. We then use the parameter inference code Monte Python to confront ThetaCDM with data from WMAP-7, SPT and WiggleZ. We obtain strong bounds on the parameters accounting for deviations from LambdaCDM. In particular, we find that the discrepancy between the gravitational constants appearing in the Poisson and Friedmann equations is constrained at the level 1.8%.Comment: 17 pages, 5 figure

Cosmological constraints on deviations from Lorentz invariance in gravity and dark matter

We consider a scenario where local Lorentz invariance is violated by the existence of a preferred time direction at every space-time point. This scenario can arise in the context of quantum gravity and its description at low energies contains a unit time-like vector field which parameterizes the preferred direction. The particle physics tests of Lorentz invariance preclude a direct coupling of this vector to the fields of the Standard Model, but do not bear implications for dark matter. We discuss how the presence of this vector and its possible coupling to dark matter affect the evolution of the Universe. At the level of homogeneous cosmology the only effect of Lorentz invariance violation is a rescaling of the expansion rate. The physics is richer at the level of perturbations. We identify three effects crucial for observations: the rescaling of the matter contribution to the Poisson equation, the appearance of an extra contribution to the anisotropic stress and the scale-dependent enhancement of dark matter clustering. These effects result in distinctive features in the power spectra of the CMB and density fluctuations. Making use of the data from Planck and WiggleZ we obtain the most stringent cosmological constraints to date on departures from Lorentz symmetry. Our analysis provides the first direct bounds on deviations from Lorentz invariance in the dark matter sector.Comment: 10 pages, 3 figures, revtex; footnote on isocurvature modes added, discussion on the decoupling of the Standard Model fields from the aether extended, a reference added; version to be published in JCA

Experimental assessment of the speed of light perturbation in free-fall absolute gravimeters

Precision absolute gravity measurements are growing in importance, especially in the context of the new definition of the kilogram. For the case of free-fall absolute gravimeters with a Michelson-type interferometer tracking the position of a free falling body, one of the effects that needs to be taken into account is the speed of light perturbation due to the finite speed of propagation of light. This effect has been extensively discussed in the past, and there is at present a disagreement between different studies. In this work, we present the analysis of new data and confirm the result expected from the theoretical analysis applied nowadays in free-fall gravimeters. We also review the standard derivations of this effect (by using phase shift or Doppler effect arguments) and show their equivalence

Horava gravity vs. thermodynamics: the black hole case

Under broad assumptions breaking of Lorentz invariance in gravitational theories leads to tension with unitarity because it allows for processes that apparently violate the second law of thermodynamics. The crucial ingredient of this argument is the existence of black hole solutions with the interior shielded from infinity by a causal horizon. We study how the paradox can be resolved in the healthy extension of Horava gravity. To this aim we analyze classical solutions describing large black holes in this theory with the emphasis on their causal structure. The notion of causality is subtle in this theory due to the presence of instantaneous interactions. Despite this fact, we find that within exact spherical symmetry a black hole solution contains a space-time region causally disconnected from infinity by a surface of finite area -- the `universal horizon'. We then consider small perturbations of arbitrary angular dependence in the black hole background. We argue that aspherical perturbations destabilize the universal horizon and, at non-linear level, turn it into a finite-area singularity. The causal structure of the region outside the singularity is trivial. If the higher-derivative terms in the equations of motion smear the singularity while preserving the trivial causal structure of the solutions, the thermodynamics paradox would be obviated. As a byproduct of our analysis we prove that the black holes do not have any non-standard long-range hair. We also comment on the relation with Einstein-aether theory, where the solutions with universal horizon appear to be stable.Comment: 36 pages, 3 figures, 1 table. v2 Small changes to agree with published versio

A healthy extension of Horava gravity

We propose a natural extension of Horava's model for quantum gravity, which is free from the notorious pathologies of the original proposal. The new model endows the scalar graviton mode with a regular quadratic action and remains power-counting renormalizable. At low energies, it reduces to a Lorentz-violating scalar-tensor gravity theory. The deviations with respect to general relativity can be made weak by an appropriate choice of parameters.Comment: 4 pages, no figure

Testing Lorentz invariance of dark matter

We study the possibility to constrain deviations from Lorentz invariance in dark matter (DM) with cosmological observations. Breaking of Lorentz invariance generically introduces new light gravitational degrees of freedom, which we represent through a dynamical timelike vector field. If DM does not obey Lorentz invariance, it couples to this vector field. We find that this coupling affects the inertial mass of small DM halos which no longer satisfy the equivalence principle. For large enough lumps of DM we identify a (chameleon) mechanism that restores the inertial mass to its standard value. As a consequence, the dynamics of gravitational clustering are modified. Two prominent effects are a scale dependent enhancement in the growth of large scale structure and a scale dependent bias between DM and baryon density perturbations. The comparison with the measured linear matter power spectrum in principle allows to bound the departure from Lorentz invariance of DM at the per cent level.Comment: 42 pages, 9 figure

Technically natural dark energy from Lorentz breaking

We construct a model of dark energy with a technically natural small contribution to cosmic acceleration, i.e. this contribution does not receive corrections from other scales in the theory. The proposed acceleration mechanism appears generically in the low-energy limit of gravity theories with violation of Lorentz invariance that contain a derivatively coupled scalar field Theta. The latter may be the Goldstone field of a broken global symmetry. The model, that we call Theta-CDM, is a valid effective field theory up to a high cutoff just a few orders of magnitude below the Planck scale. Furthermore, it can be ultraviolet-completed in the context of Horava gravity. We discuss the observational predictions of the model. Even in the absence of a cosmological constant term, the expansion history of the Universe is essentially indistinguishable from that of Lambda-CDM. The difference between the two theories appears at the level of cosmological perturbations. We find that in Theta-CDM the matter power spectrum is enhanced at subhorizon scales compared to Lambda-CDM. This property can be used to discriminate the model from Lambda-CDM with current cosmological data.Comment: A few equations in the Appendix correcte

On the Extra Mode and Inconsistency of Horava Gravity

We address the consistency of Horava's proposal for a theory of quantum gravity from the low-energy perspective. We uncover the additional scalar degree of freedom arising from the explicit breaking of the general covariance and study its properties. The analysis is performed both in the original formulation of the theory and in the Stueckelberg picture. A peculiarity of the new mode is that it satisfies an equation of motion that is of first order in time derivatives. At linear level the mode is manifest only around spatially inhomogeneous and time-dependent backgrounds. We find two serious problems associated with this mode. First, the mode develops very fast exponential instabilities at short distances. Second, it becomes strongly coupled at an extremely low cutoff scale. We also discuss the "projectable" version of Horava's proposal and argue that this version can be understood as a certain limit of the ghost condensate model. The theory is still problematic since the additional field generically forms caustics and, again, has a very low strong coupling scale. We clarify some subtleties that arise in the application of the Stueckelberg formalism to Horava's model due to its non-relativistic nature.Comment: Discussion expanded; a figure added; accepted to JHE

Supersymmetric Aether

It has been suggested by Groot Nibbelink and Pospelov that Lorentz invariance can be an emergent symmetry of low-energy physics provided the theory enjoys a non-relativistic version of supersymmetry. We construct a model that realizes the latter symmetry dynamically: it breaks Lorentz invariance but leaves the supersymmetry generators intact. The model is a supersymmetric extension of the dynamical aether theory of Jacobson and Mattingly. It shows rich dynamics and possesses a family of inequivalent vacua realizing different symmetry breaking patterns. In particular, we find stable vacua that break spontaneously spatial isotropy. Supersymmetry breaking terms give masses to fermionic and bosonic partners of the aether field. We comment on the coupling of the model to supergravity and on the implications for Horava gravity.Comment: 21 pages, no figure