Horava-Lifshitz Gravity Research Articles

Observational Data Fitting to Constrain Variable Modified Chaplygin Gas in the Background of Horava-Lifshitz Gravity

FRW universe in Horava-Lifshitz (HL) gravity model filled with a combination of dark matter and dark energy in the form of variable modified Chaplygin gas (VMCG) is considered. The permitted values of the VMCG parameters are determined by the recent astrophysical and cosmological observational data. Here we present the Hubble parameter in terms of the observable parameters Ω d m0, Ω v m c g0, H 0, redshift z and other parameters like α, A, γ and n. From Stern data set (12 points), we have obtained the bounds of the arbitrary parameters by minimizing the χ 2 test. The best-fit values of the parameters are obtained by 66 %, 90 % and 99 % confidence levels. Next due to joint analysis with BAO and CMB observations, we have also obtained the bounds of the parameters (A, γ) by fixing some other parameters α and n. The best fit value of distance modulus μ(z) is obtained for the VMCG model in HL gravity, and it is concluded that our model is perfectly consistent with the union2 sample data.

Power-counting and renormalizability in Lifshitz scalar theory

We study the renormalizability in theories of a self-interacting Lifshitz scalar field. We show that although the statement of power-counting is true at one-loop order, in generic cases where the scalar field is dimensionless, an infinite number of counter terms are involved in the renormalization procedure. This problem can be avoided by imposing symmetries, the shift symmetry in the present paper, which allow only a finite number of counter terms to appear. The symmetry requirements might have important implications for the construction of matter field sectors in the Horava-Lifshitz gravity.

Generalized entropies and the expansion law of the universe

We suggest that using the first law of thermodynamics is a convenient method to obtain a correct form of the expansion law of the universe \cite{T. Padmanabhan1}. We will, then, use this idea to obtain the expansion law for a Kodama observer. By using the expansion law for a Kodama observer, we can obtain the dynamic equation of the FRW universe for deformed Horava-Lifshitz gravity. The use of the first law of thermodynamics also leads to a new approach for obtaining the Friedmann equations for f(R) and scalar tensor gravities.

Inflationary gravitational waves in the effective field theory of modified gravity

In the approach of the effective field theory of modified gravity, we derive the second-order action and the equation of motion for tensor perturbations on the flat isotropic cosmological background. This analysis accommodates a wide range of gravitational theories including Horndeski theories, its generalization, and the theories with spatial derivatives higher than second order (e.g., Horava-Lifshitz gravity). We obtain the inflationary power spectrum of tensor modes by taking into account corrections induced by higher-order spatial derivatives and slow-roll corrections to the de Sitter background. We also show that the leading-order spectrum in concrete modified gravitational theories can be mapped on to that in General Relativity under a disformal transformation. Our general formula will be useful to constrain inflationary models from the future precise measurement of the B-mode polarization in the cosmic microwave background.

Post-Newtonian constraints on Lorentz-violating gravity theories with a MOND phenomenology

We study the post-Newtonian expansion of a class of Lorentz-violating gravity theories that reduce to khronometric theory (i.e. the infrared limit of Horava gravity) in high-acceleration regimes, and reproduce the phenomenology of the modified Newtonian dynamics (MOND) in the low-acceleration, non-relativistic limit. Like in khronometric theory, Lorentz symmetry is violated in these theories by introducing a dynamical scalar field (the "khronon") whose gradient is enforced to be timelike. As a result, hypersurfaces of constant khronon define a preferred foliation of the spacetime, and the khronon can be thought of as a physical absolute time. The MOND phenomenology arises as a result of the presence, in the action, of terms depending on the acceleration of the congruence orthogonal to the preferred foliation. We find that if the theory is forced to reduce exactly to General Relativity (rather than to khronometric theory) in the high-acceleration regime, the post-Newtonian expansion breaks down at low accelerations, and the theory becomes strongly coupled. Nevertheless, we identify a sizeable region of the parameter space where the post-Newtonian expansion remains perturbative for all accelerations, and the theory passes both solar-system and pulsar gravity tests, besides producing a MOND phenomenology for the rotation curves of galaxies. We illustrate this explicitly with a toy model of a system containing only baryonic matter but no Dark Matter.

Casimir effect in the Hořava–Lifshitz gravity with a cosmological constant

We calculate the Casimir 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. To this end, we take into account a static and spherically symmetric solution of Hořava–Lifshitz (HL) gravity, with a cosmological constant term, in lower orders of approximation, considering both weak-field and infrared limits. We show that the Casimir energy, just in the second order weak-field approximation, is modified due to the parameter of the HL gravity as well as to the cosmological constant.

A proposal for testing gravity's rainbow

Various approaches to quantum gravity such as string theory, loop quantum gravity and Horava-Lifshitz gravity predict modifications of the energy-momentum dispersion relation. Magueijo and Smolin incorporated the modified dispersion relation (MDR) with the general theory of relativity to yield a theory of gravity's rainbow. In this paper, we investigate the Schwarzschild metric in the context of gravity's rainbow. We investigate rainbow functions from three known modified dispersion relations that were introduced by Amelino-Camelia et al. (in Int. J. Mod. Phys. A, 12 (1997) 607; Living Rev. Relativ., 16 (2013) 5; Nature, 393 (1998) 763) and by Magueijo-Smolin (in Phys. Rev. Lett., 88 (2002) 190403). We study the effect of the rainbow functions on the deflection of light, photon time delay, gravitational red-shift, and the weak-equivalence principle. We compare our results with experiments to obtain upper bounds on the parameters of the rainbow functions.

Two-dimensional Horava-Lifshitz black hole solutions

In this paper we address the issue of black hole solutions in (1+1)-dimensional non-projectable Horava-Lifshitz gravity. We consider several models by considering different potentials in the scalar matter sector. We also consider the gravitational collapse of a distribution of pressureless dust filling a region in one-dimensional space. The time of the collapse can be faster or slower depending on the parameter $\lambda$ of the theory.

Hořava gravity with mixed derivative terms

Horava gravity has been constructed so as to exhibit anisotropic scaling in the ultraviolet, as this renders the theory power-counting renormalizable. However, when coupled to matter, the theory has been shown to suffer from quadratic divergences. A way to cure these divergences is to add terms with both time and space derivatives. We consider this extended version of the theory in detail. We perform a perturbative analysis that includes all modes, determine the propagators and discuss how including mixed-derivative terms affects them. We also consider the Lifshitz scalar with mixed-derivative terms as a toy model for power counting arguments and discuss the influence of such terms on renormalizability.

Brane structure from a scalar field in general covariant Horava-Lifshitz gravity

In this paper we have considered the structure of the non-projectable Horava-Melby-Thompson (HMT) gravity to find braneworld scenarios. A relativistic scalar field is considered in the matter sector and we have shown how to reduce the equations of motion to first-order differential equations. In particular, we have studied thick brane solutions of both the dilatonic and Randall-Sundrum types.

Asymptotically hyperbolic black holes in Horava gravity

Solutions of Hořava gravity that are asymptotically Lifshitz are explored. General near boundary expansions allow the calculation of the mass of these spacetimes via a Hamiltonian method. Both analytic and numeric solutions are studied which exhibit a causal boundary called the universal horizon, and are therefore black holes of the theory. The thermodynamics of an asymptotically Anti-de Sitter Hořava black hole are verified.

Hořava-Lifshitz gravity and effective theory of the fractional quantum Hall effect

We show that Horava-Lifshitz gravity theory can be employed as a covariant framework to build an effective field theory for the fractional quantum Hall effect that respects all the spacetime symmetries such as non-relativistic diffeomorphism invariance and anisotropic Weyl invariance as well as the gauge symmetry. The key to this formalism is a set of correspondence relations that maps all the field degrees of freedom in the Horava-Lifshitz gravity theory to external background (source) fields among others in the effective action of the quantum Hall effect, according to their symmetry transformation properties. We originally derive the map as a holographic dictionary, but its form is independent of the existence of holographic duality. This paves the way for the application of Horava-Lifshitz holography on fractional quantum Hall effect. Using the simplest holographic Chern-Simons model, we compute the low energy effective action at leading orders and show that it captures universal electromagnetic and geometric properties of quantum Hall states, including the Wen-Zee shift, Hall viscosity, angular momentum density and their relations. We identify the shift function in Horava-Lifshitz gravity theory as minus of guiding center velocity and conjugate to guiding center momentum. This enables us to distinguish guiding center angular momentum density from the internal one, which is the sum of Landau orbit spin and intrinsic (topological) spin of the composite particles. Our effective action shows that Hall viscosity is minus half of the internal angular momentum density and proportional to Wen-Zee shift, and Hall bulk viscosity is half of the guiding center angular momentum density.

Role of the extra coupling in the kinetic term in Hořava-Lifshitz gravity

We analyze different claims on the role of the coupling constant lambda in so-called lambda-R models, a minimal generalization of general relativity inspired by Horava-Lifshitz gravity. The dimensionless parameter lambda appears in the kinetic term of the Einstein-Hilbert action, leading to a one-parameter family of classical theories. Performing a canonical constraint analysis for closed spatial hypersurfaces, we obtain a result analogous to that of Bellorin and Restuccia, who showed that all non-projectable lambda-R models are equivalent to general relativity in the asymptotically flat case. However, the tertiary constraint present for closed boundary conditions assumes a more general form. We juxtapose this with an earlier finding by Giulini and Kiefer, who ruled out a range of lambda-R models by a physical, cosmological argument. We show that their analysis can be interpreted consistently within the projectable sector of Horava-Lifshitz gravity, thus resolving the apparent contradiction.

A unifying description of dark energy

We review and extend a novel approach that we recently introduced, to describe general dark energy or scalar-tensor models. Our approach relies on an Arnowitt-Deser-Misner (ADM) formulation based on the hypersurfaces where the underlying scalar field is uniform. The advantage of this approach is that it can describe in the same language and in a minimal way a vast number of existing models, such as quintessence, F(R) theories, scalar tensor theories, their Horndeski extensions and beyond. It also naturally includes Horava–Lifshitz theories. As summarized in this review, our approach provides a unified treatment of the linear cosmological perturbations about a Friedmann-Lemaître-Robertson-Walker (FLRW) universe, obtained by a systematic expansion of our general action up to quadratic order. This shows that the behavior of these linear perturbations is generically characterized by five time-dependent functions. We derive the full equations of motion in the Newtonian gauge. In the Horndeski case, we obtain the equation of state for dark energy perturbations in terms of these functions. Our unifying description thus provides the simplest and most systematic way to confront theoretical models with current and future cosmological observations.

Universal horizons and black holes in gravitational theories with broken Lorentz symmetry

In this paper, we first show that the definition of the universal horizons studied recently in the khronometric theory of gravity can be straightforwardly generalized to other theories that violate the Lorentz symmetry, by simply considering the khronon as a probe field and playing the same role as a Killing vector field. As an application, we study static charged (D + 1)-dimensional spacetimes in the framework of the healthy (nonprojectable) Horava–Lifshitz (HL) gravity in the infrared (IR) limit, and find various solutions. Some of them represent Lifshitz spacetimes with hyperscaling violations, and some have black hole structures. In the latter, universal horizons always exist inside the Killing horizons. The surface gravity on them can be either larger or smaller than the surface gravity on the Killing horizons, depending on the spacetimes considered. Although such black holes are found only in the IR, we argue that black holes with universal horizons also exist in the full theory of the HL gravity. A simple example is the Schwarzschild solution written in the Painleve–Gullstrand coordinates, which is also a solution of the full theory of the HL gravity and has a universal horizon located inside the Schwarzschild Killing horizon.

A Slowly Rotating Black Hole in Horava-Lifshitz Gravity and a 3+1 Dimensional Topological Black Hole: Motion of Particles and BSW Mechanism

The motion of a neutral particle in the vicinity of a slowly rotating black hole in the Horava-Lifshitz theory of gravity and 3+1 dimensional topological Lifshitz black hole is investigated. Geodesics for radial motion of the particles are also plotted. Some different cases of the orbital motion of the particle are discussed where maximum and minimum values of the effective potential are calculated. Further the Ba\~{n}ados, Silk and West (BSW) mechanism is studied for these black holes. It is shown that the centre-of-mass energy (CME) of two colliding uncharged particles at the horizon of these black holes remains finite. Thus the BSW effect cannot be seen in these cases.

Asymptotic freedom in Hořava-Lifshitz gravity.

We use the Wetterich equation for foliated spacetimes to study the renormalization group flow of projectable Hořava-Lifshitz gravity coupled to n Lifshitz scalars. Using novel results for anisotropic heat kernels, the matter-induced beta functions for the gravitational couplings are computed explicitly. The renormalization group flow exhibits an UV attractive anisotropic Gaussian fixed point where Newton's constant vanishes and the extra scalar mode decouples. This fixed point ensures that the theory is asymptotically free in the large-n expansion, indicating that projectable Hořava-Lifshitz gravity is perturbatively renormalizable. Notably, the fundamental fixed point action does not obey detailed balance.

On geodesics in space-times with a foliation structure: a spectral geometry approach

Motivated by the Horava–Lifshitz (HL)-type theories, we study the physical motion of matter coupled to a foliated geometry in a non-diffeomorphism invariant way. We use the concept of a spectral action as a guiding principle in writing down the matter action. Based on the deformed Dirac operator compatible with the reduced symmetry-foliation preserving diffeomorphisms, this approach provides a natural generalization of the minimal coupling. Focusing on the infrared version of the Dirac operator, we derive the physical motion of a test particle and discuss in what sense it can still be considered as a geodesic motion for some modified geometry. We show that the apparatus of non-commutative geometry could be very efficient in the study of matter coupled to the HL gravity.

Reconstruction of $$f(\tilde R)$$ models via well-known scale factors

We explore the reconstruction scheme of new holographic dark energy and modified f(R) Horava-Lifshitz gravity $$(f(\tilde R))$$ in the presence of three well-known scale factors such as the emergent, logamediate and intermediate ones. We analyze the behavior of reconstructed $$f(\tilde R)$$ models corresponding to these scale factors. We also present the analysis of the equation of state parameter which shows consistency with the present cosmological scenario. The squared speed of sound is also developed in this framework for analyzing the instability of the reconstructed $$f(\tilde R)$$ models for all scale factors.

Energy of a slowly-rotating black hole in Horava-Lifshitz gravity by using approximate Lie symmetry methods

The energy content of the Lee-Kim-Myung slowly-rotating black hole (Lee et al., Eur. Phys. J. C 70, 361 (2010)), in the Horava-Lifshitz (HL) theory of gravity is investigated by using approximate Lie symmetry methods for differential equations. The energy of this slowly-rotating black hole in the HL gravity is found to be is rescaled by a r-dependent factor. From the rescaling of energy, the rotation is observed to be added to the mass of the black hole, and this effect decreases with increasing coordinate r. This expression of energy rescaling reduces to the Schwarzschild mass for the limits in which the Lee-Kim-Myung slowly rotating black hole solution in the HL gravity reduces to the Schwarzschild solution in general relativity.