Horava-Lifshitz Gravity Research Articles

Thermal tachyacoustic cosmology

An intriguing possibility that can address pathologies in both early universe cosmology (i.e. the horizon problem) and quantum gravity (i.e. non-renormalizability), is that particles at very high energies and/or temperatures could propagate arbitrarily fast. A concrete realization of this possibility for the early universe is the Tachyacoustic (or Speedy Sound) cosmology, which could also produce a scale-invariant spectrum for scalar cosmological perturbations. Here, we study Thermal Tachyacoustic Cosmology (TTC), i.e. this scenario with thermal initial conditions. We find that a phase transition in the early universe, around the scale of Grand Unified Theories (GUT scale; $T\sim 10^{15}$ GeV), during which the speed of sound drops by $25$ orders of magnitude within a Hubble time, can fit current CMB observations. We further discuss how production of primordial black holes constrains the cosmological acoustic history, while coupling TTC to Horava-Lifshitz gravity leads to a lower limit on the amplitude of tensor modes ($r \gtrsim 10^{-3}$), that are detectable by CMBPol (and might have already been seen by the BICEP-Keck collaboration).

Planck-scale dimensional reduction without a preferred frame

Several approaches to quantum gravity suggest that the standard description of spacetime as probed at low-energy, with four dimensions, is replaced in the Planckian regime by a spacetime with a spectral dimension of two. The implications for relativistic symmetries can be momentous, and indeed the most tangible picture for “running” of the spectral dimension, found within Horava–Lifshitz gravity, requires the breakdown of relativity of inertial frames. In this Letter we incorporate running spectral dimensions in a scenario that does not require the emergence of a preferred frame. We consider the best studied mechanism for deforming relativistic symmetries whilst preserving the relativity of inertial frames, based on a momentum space with curvature at the Planck scale. We show explicitly how running of the spectral dimension can be derived from these models.

Observational Constraints of Red-shift Parametrization Parameters of Dark Energy in Horava-Lifshitz Gravity

We have assumed that the FRW universe filled with baryonic matter, radiation and dark matter along with dark energy in the frame-work of Horava-Lifshitz gravity. Here three parameterizations like Linear, CPL and JBP for the dark energy have been assumed for the variations of EOS parameter w(z). The observational data analysis by χ2 minimum test have been analyzed for our models. From Stern, Stern+BAO and Stern+BAO+CMB joint data analysis, we have obtained the bounds of the arbitrary parameters w0 and w1. The best fit values of the parameters w0 and w1 for these three models and the minimum values of χ2 have been obtained by observational data analysis. Also the bounds of the parameters w0 and w1 are obtained by 66 %, 90 % and 99 % confidence levels for linear, CPL and JBP models. Next red shift-magnitude observational data points from type Ia supernovae have been considered and which contains 557 data points. From this observation, the distance modulus μ(z) against red shift z has been investigated for our predicted theoretical model (three DE models) for the best fit values of the parameters and the observed SNe Ia Union2 data sample. Finally, we have investigated that our predicted theoretical three models permitted the observational data sets.

Vaidya solutions in general covariant Hořava–Lifshitz gravity without projectability: Infrared limit

In this paper, we have studied nonstationary radiative spherically symmetric spacetime, in general covariant theory (U(1) extension) of Hořava–Lifshitz (HL) gravity without the projectability condition and in the infrared (IR) limit. The Newtonian prepotential φ was assumed null. We have shown that there is not the analogue of the Vaidya's solution in the Hořava–Lifshitz Theory (HLT), as we know in the General Relativity Theory (GRT). Therefore, we conclude that the gauge field A should interact with the null radiation field of the Vaidya's spacetime in the HLT.

New holographic dark energy in modified f(R) Horava-Lifshitz gravity

In this paper, we study the new holographic dark energy model in the framework of modified f(R) Horava-Lifshitz Gravity. We apply correspondence scheme to construct model the in underlying scenario using power-law form of scale factor. To explore accelerated expansion of the universe, some well-known cosmological parameters (equation of state parameter and squared speed of sound) and cosmological planes (ωΛ–\(\omega'_{\varLambda}\) and statefinder) are discussed for reconstructed model. It is interesting to conclude that these parameters represent phantom behavior of the universe with stable configuration. also, the cosmological planes show compatible results with recent observations for accelerated expansion of the universe.

Electric–Magnetic duality in (linearized) Hořava–Lifshitz gravity

We present an implementation of a duality symmetry in the minimal linearized Hořava–Lifshitz gravity. Some difficulties arise when an attempt is made to implement off shell duality symmetries in theories that are not invariant under full spacetime diffeomorphisms. To avoid some of them our approach will consist of two steps: a) Proposing an explicit formulation of a covariant model and applying standard rules to relate a theory with its dual, and b) Implementing a projection of this covariant model to Horava–Lifshitz gravity using a gauge fixing condition. In this way we are able to present a dual action of the standard formulation of minimal linearized Horava–Lifshitz gravity.

Conformally Lifshitz solutions from Horava–Lifshitz Gravity

We show that the IR action of the healthy non-projectable Hořava–Lifshitz gravity and its small modification exhibit Lifshitz and hyperscaling violating solutions, respectively, though it does not have the corresponding static black hole solutions. The model may also have an AdS2 × Rd vacuum solution.

Dynamical emergence of universal horizons during the formation of black holes

Motivations for the existence of a fundamental preferred frame range from pure phenomenology to attempts to solve the non-renormalizability of quantum gravity, the problem of time (and scale), and the cosmological constant problem(s). In many explicit constructions, such as Einstein-Aether or Gravitational Aether theories, K-essence, Cuscuton theory, Shape Dynamics, or (non-projectable) Horava-Lifshitz gravity, the low energy theory contains a fluid (which defines a preferred frame) with superluminal or incompressible excitations. We study here the formation of black holes in the presence of such a fluid. In particular, we focus on the incompressible limit of the fluid (or Constant Mean Curvature foliation) in the space-time of a spherically collapsing shell within an asymptotically cosmological space-time. In this case, ignoring the fluid back reaction, we can analytically show that an observer inside 3/4 of the Schwarzschild radius cannot send a signal outside, after a stage in collapse, even using signals that propagate infinitely fast in the preferred frame. This confirms the dynamical emergence of universal horizons that have been previously found in static solutions. We argue that this universal horizon should be considered as the future boundary of the classical space-time.

Charged black holes in Hořava gravity

We explore static spherically symmetric black hole solutions allowing a bulk U(1) vector field in the khronometric formulation of Horava gravity by way of Einstein-Aether. We examine analytic solutions and study numerical results in the limit that the khronon does not backreact on the metric.

Covariant renormalizable modified and massive gravity theories on (non)commutative tangent Lorentz bundles

The fundamental field equations in modified gravity (including general relativity; massive and bimetric theories; Hořava–Lifshitz (HL); Einstein–Finsler gravity extensions etc.) possess an important decoupling property with respect to nonholonomic frames with 2 (or 3) + 2 + 2 + ⋯ spacetime decompositions. This allows us to construct exact solutions with generic off-diagonal metrics depending on all spacetime coordinates via generating and integration functions containing (un-)broken symmetry parameters. Such nonholonomic configurations/models have a nice ultraviolet behavior and seem to be ghost-free and (super-)renormalizable in a sense of covariant and/or massive modifications of HL gravity. The apparent noncommutativity and breaking of Lorentz invariance by quantum effects can be encoded into fibers of noncommutative tangent Lorentz bundles for corresponding "partner" anisotropically induced theories. We show how the constructions can be extended to include conjectured covariant renormalizable models with massive graviton fields and effective Einstein fields with (non)commutative variables.

On nonrelativistic diffeomorphism invariance

We study certain aspects of the recently proposed notion of nonrelativistic diffeomorphism invariance. In particular, we consider specific examples of invariant actions, extended gauge symmetry as well as an application to the theory of quantum Hall effect. We also discuss an alternative approach based on Horava-Lifshitz gravity.

Power-law solution of new agegraphic modified f(R) Horava-Lifshitz gravity

We study the reconstruction scenario of modified gravity with a dynamical dark-energy model filling the universe. In this context, we consider the Modified f(R) Horava-Lifshitz Gravity with a new agegraphic dark-energy model using the power-law form of the scale factor. We construct a modified f(R) Horava-Lifshitz model and check its behavior along its argument. To discuss the accelerated expansion of the universe, some cosmological parameters are discussed as well. The equation-of-state parameter represents the phantom behavior of the universe as well as the statefinder diagnostic pair gives the phantom and quintessence regions. Also, the stability analysis is carried out through squared speed of sound which points out the stable modified f(R) Horava-Lifshitz model except in a small time interval.

General Relativity without paradigm of space-time covariance, and resolution of the problem of time

The framework of a theory of gravity from the quantum to the classical regime is presented. The paradigm shift from full space-time covariance to spatial diffeomorphism invariance, together with clean decomposition of the canonical structure, yield transparent physical dynamics and a resolution of the problem of time. The deep divide between quantum mechanics and conventional canonical formulations of quantum gravity is overcome with a Schrodinger equation for quantum geometrodynamics that describes evolution in intrinsic time. Unitary time development with gauge-invariant temporal ordering is also viable. All Kuchar observables become physical; and classical space-time, with direct correlation between its proper times and intrinsic time intervals, emerges from constructive interference. The framework not only yields a physical Hamiltonian for Einstein’s theory, but also prompts natural extensions and improvements towards a well behaved quantum theory of gravity. It is a consistent canonical scheme to discuss Horava–Lifshitz theories with intrinsic time evolution, and of the many possible alternatives that respect 3-covariance (rather thanthemorerestrictive4-covariance ofEinstein’stheory), Horava’s “detailed balance” form of the Hamiltonian constraint is essentially pinned down by this framework. Issues in quantum gravity that depend on radiative corrections and the rigorous definition and regularization of the Hamiltonian operator are not addressed in this work.

Hořava-Lifshitz gravity effects on Casimir energy in weak field approximation and infrared regime

We calculate the renormalized vacuum energy of a massless scalar field confined between two nearby parallel plates formed by ideal uncharged conductors, placed tangentially to the surface of a sphere with mass M and radius R. This study will take into account the static and spherically symmetric solution of Horava-Lifshitz gravity found by Kehagias-Sfetsos (KS), in both weak field and infrared limits. A slight amplification of the Casimir force between the conducting plates is found. Thermal corrections to the Casimir energy are analyzed. Based on current Casimir effect measurements, a constraint on the $\omega$ parameter of KS metric is also obtained.

Emergent Horava gravity in graphene

First of all, we reconsider the tight-binding model of monolayer graphene, in which the variations of the hopping parameters are allowed. We demonstrate that the emergent 2D Weitzenbock geometry as well as the emergent U(1) gauge field appear. The emergent gauge field is equal to the linear combination of the components of the zweibein. Therefore, we actually deal with the gauge fixed version of the emergent 2+1 D teleparallel gravity. In particular, we work out the case, when the variations of the hopping parameters are due to the elastic deformations, and relate the elastic deformations with the emergent zweibein. Next, we investigate the tight-binding model with the varying intralayer hopping parameters for the multilayer graphene with the ABC stacking. In this case the emergent 2D Weitzenbock geometry and the emergent U(1) gauge field appear as well, and the emergent low energy effective field theory has the anisotropic scaling.

A unified phase transition picture of the charged topological black hole in Hořava-Lifshitz gravity

Aiming at a unified phase transition picture of the charged topological black hole in Ho\v{r}ava-Lifshitz gravity, we investigate this issue not only in canonical ensemble with the fixed charge case but also in grand-canonical ensemble with the fixed potential case. We firstly perform the standard analysis of the specific heat, the free energy and the Gibbs potential, and then study its geometrothermodynamics. It is shown that the local phase transition points not only witness the divergence of the specific heat, but also witness the minimum temperature and the maximum free energy or Gibbs potential. They also witness the divergence of the corresponding thermodynamic scalar curvature. No matter which ensemble is chosen, the metric constructed can successfully produce the behavior of the thermodynamic interaction and phase transition structure while other metrics failed to predict the phase transition point of the charged topological black hole in former literature. In grand-canonical ensemble, we have discovered the phase transition which has not been reported before. It is similar to the canonical ensemble in which the phase transition only takes place when $k=-1$. But it also has its unique characteristics that the location of the phase transition point depends on the value of potential, which is different from the canonical ensemble where the phase transition point is independent of the parameters. After an analytical check of Ehrenfest scheme, we find that the new phase transition is a second order one. It is also found that the thermodynamics of the black hole in Horava-Lifshitz gravity is quite different from that in Einstein gravity.

Observational constraints on modified Chaplygin gas in Horava–Lifshitz gravity with dark radiation

We present Cosmological models with modified Chaplygin gas (MCG) in the framework of Horava-Lifshitz (HL) theory of gravity both with and without detailed balance. The equation of state (EOS) for a MCG contains three unknown parameters namely, $A$, $\alpha$, $B$. The allowed values of some of these parameters of the EOS are determined using the recent astrophysical and cosmological observational data. Using observational data from $H(z)-z$, BAO peak parameter, CMB shift parameter we study cosmologies in detailed-balance and beyond detailed-balance scenario. In this paper we take up the beyond detailed-balance scenario in totality and contribution of dark radiation in the case of detailed-balance scenario on the parameters of the EOS. We explore the effect of dark radiation on the whole range the of effective neutrino parameter to constrain matter contributing parameter $B$ in both the detailed-balance and the beyond-detailed balance scenario. It has been observed that greater the dark radiation less the matter contribution in the MCG in both the scenario considered here. In order to check the validity of beyond detailed balance scenario we plot supernovae magnitudes ($\mu$) with redshift of Union2 data and then the variation of state parameter with redshift is studied. It has been observed that beyond detailed balance scenario is equally suitable in HL gravity with MCG.

Contracted Lorentz invariance for gravity with a preferred foliation

In canonical gravity, the choice of a local time direction is not obviously compatible with local Lorentz invariance. One way to address this issue is to view gravity as a gauge theory on observer space, rather than spacetime. In a Lorentz covariant theory observer space is the space of unit future-directed timelike vectors; picking such a vector locally breaks the symmetry to a subgroup SO(D) of SO(D,1), so that on observer space the local symmetry group is SO(D). Observer space geometries naturally describe any gravitational theory that only assumes local invariance under SO(D). Here we construct nonrelativistic observer spaces for gravity with a fixed foliation, applicable to preferred foliation theories such as Horava-Lifshitz gravity. Different Horava-Lifshitz observers at a point are related by a change in the shift vector, leaving the preferred foliation invariant. Gravity is formulated on a non-relativistic frame bundle with structure group ISO(D); the shift vector acts as a symmetry breaking field breaking ISO(D) symmetry spontaneously to SO(D). A natural torsion-free connection is constructed, including the usual SO(D,1) connection of relativistic gravity plus terms depending on derivatives of the shift vector. This observer space geometry provides a novel geometric framework for the study of preferred foliation theories.

Polarizing primordial gravitational waves by parity violation

We study primordial gravitational waves in the Horava-Lifshitz theory of quantum gravity, in which high-order spatial derivative operators, including the ones violating parity, generically appear in order for the theory to be power-counting renormalizable and ultraviolet complete. Because of both parity violation and the nonadiabatic evolution of the modes due to a modified dispersion relationship, a large polarization of primordial gravitational waves becomes possible, and it could be well within the range of detection of the BB, TB and EB power spectra of the forthcoming cosmic microwave background observation, where T, E, and B stand, respectively, the different components of the polarization of the cosmic microwave background radiation.

A holographic reconstruction of the modified f(R) Horava-Lifshitz gravity with scale factor in power-law form

This paper is devoted to the study of holographic reconstruction of the modified f(R) Horava-Lifshitz gravity in the flat universe. For this purpose, we assume a scale factor in the form of exact power-law solution. A reconstructed model is obtained which may provide reasonable qualitative description of some cosmological era satisfying the sufficient condition for a realistic model. We represent the graphical description of this model exhibiting increasing behavior. We also discuss the evolution of the accelerated expansion of the universe through equation of state parameter (EoS) for the reconstructed model. Its graphical representation depicts about a quintessence dominated era in near future. The stability of the model is observed initially, however it becomes unstable after a small interval of time.