Fabao Gao, Jaume Llibre
When the cosmological constant is non-zero the dynamics of the cosmological model based on Horava-Lifshitz gravity in a non-flat universe is characterized by using the qualitative theory of differential equations.
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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.
Both projectable and non-projectable versions of Horava-Lifshitz gravity face serious challenges. In the non-projectable version, the constraint algebra is seemingly inconsistent. The projectable version lacks a local Hamiltonian constraint, thus allowing for an extra scalar mode which can be problematic. A new formulation of non-projectable Horava-Lifshitz gravity, naturally realized as a representation of the master constraint algebra studied by loop quantum gravity researchers, is presented. This yields a consistent canonical theory with first class constraints. It captures the essence of H…
We initiate the study of Horava-Lifshitz models of gravity in the framework of spectral geometry. As the first step, we calculate the dimension of space-time. It is shown, that for the natural choice of a Dirac operator (or rather corresponding generalized Laplacian), which respects both the foliation structure and anisotropic scaling, the result of Horava on a spectral dimension is reproduced for an arbitrary, non-flat space-time. The advantage and further applications of our approach are discussed.
We give a brief exposition of the approach based on the methods of spectral geometry and the spectral action principle to construction and analysis of models on a foliated space-time.
In this letter it is shown that the Horava-Lifshitz gravity theory admits Lorentz symmetry preserving preferred global time foliation of the spacetime.
We study Euclidean wormholes in the framework of the Horava-Lifshitz theory of gravity. Euclidean wormholes first appeared in the Euclidean path integral approach to quantum gravity. In a more general way, Hawking and Page interpreted such configurations as solutions to the Wheeler-DeWitt equation with appropriate boundary conditions. We use the projectable version of Horava-Lifshitz gravity to obtain the Wheeler-DeWitt equation of a minisuperspace model considering a closed Friedmann Universe plus a massless scalar field. For large values of the scale factor we find that the solution of the W…
We construct Horava-Lifshitz gravities that are invariant under anisotropic Weyl scaling. This construction is based on an extension of the group of symmetries of healthy extended Horava-Lifshitz gravity and RFDiff invariant Horava-Lifshitz gravity. We find their Hamiltonian formulation and determine their constraint structure.
We continue our study of Horava-Lifshitz type theories using the methods of the spectral geometry. In this work we construct the infrared action of gravity and matter coupled to gravity in the most general way respecting the foliation preserving diffeomorphisms. This is done with the help of the spectral action principle based on some generalized Dirac operator. The gravity part reproduces the infrared limit of the Horava-Lifshitz gravity, while the matter part gives the generalization of the earlier suggested models. Due to the fact that the same Dirac operator is used in the construction of …
In this paper we formulate RFDiff invariant f(R) Horava-Lifshitz gravity and we show that it is related to the ghost condensation in the projectable version of Horava-Lifshitz gravity.
We study z=4 Topological black hole in 4+1 dimensional Horava-Lifshitz gravity and we calculate analytically the quasinormal modes of scalar perturbations and from these quasinormal modes we show that z=4 Topological black hole in 4+1 dimensional Horava-Lifshitz gravity is stable.
Classical and quantum Friedmann-Lemaître-Robertson-Walker universes filled with non-interacting radiation and dust fluids are considered in the framework of Hořava-Lifshitz gravity theory. The Hořava-Lifshitz theory is set in its projectable version and without detailed balance condition. Canonical quantization is performed in the Wheeler-DeWitt approach of quantum cosmology for a minisuperspace model in the light of de Broglie-Bohm interpretation of quantum mechanics. The main results are analytical solutions for non-singular quantum bounce and cyclic universes for open and closed spatial sec…
Penrose process on rotational energy extraction of the black hole (BH) in the original non-projectable Hořava-Lifshitz gravity is studied. The strong dependence of the extracted energy from the special range of parameters of the Hořava-Lifshitz gravity, such as parameter $Λ_W$ and specific angular momentum $a$ has been found. Particle acceleration near the rotating BH in Hořava-Lifshitz gravity has been studied. It is shown that the fundamental parameter of the Hořava-Lifshitz gravity can impose limitation on the the energy of the accelerating particles preventing them from the infinite value.
The effects of Horava-Lifshitz corrections to the gravito-magnetic field are analyzed. Solutions in the weak field, slow motion limit, referring to the motion of a satellite around the Earth are considered. The post-newtonian paradigm is used to evaluate constraints on the Horava-Lifshitz parameter space from current satellite and terrestrial experiments data. In particular, we focus on GRAVITY PROBE B, LAGEOS and the more recent LARES mission, as well as a forthcoming terrestrial project, GINGER.
We investigate the Hawking radiation of 3+1 and 4+1 dimensional black holes in the $z = 4$ Horava-Lifshitz gravity with fermion tunnelling. It turns out that the Hawking temperatures are recovered and are in consistence with those obtained by calculating surface gravity of the black holes. For the 3+1 dimensional black holes, the Hawking temperatures are related to the fundamental parameters of Horava-Lifshitz gravity.
We consider RFDiff invariant Horava-Lifshitz gravity action with additional Lagrange multiplier term that is a function of scalar curvature. We find its Hamiltonian formulation and we show that the constraint structure implies the same number of physical degrees of freedom as in General Relativity.
In this work, we have considered Cardassian Universe in Horava-Lifshitz gravity. Four types of Cardassian Universe models i.e., polytropic/power law, modified polytropic, exponential and modified exponential models have been considered for accelerating models. The natures of statefinder parameters, deceleration parameter, Om diagnostic and EoS parameters have been investigated for all types of Cardassian models in Horava-Lifshitz gravity.
We argue that the true nature of the renormalizability of Horava-Lifshitz gravity lies in the presence of higher order spatial derivatives and not in the anisotropic Lifshitz scaling of space and time. We discuss the possibility of constructing a higher order spatial derivatives model that has the same renormalization properties of Horava-Lifshitz gravity but that does not make use of the Lifshitz scaling. In addition, the state-of-the-art of the Lorentz symmetry restoration in Horava-Lifshitz-type theories of gravitation is reviewed.
Using the multiplicity of solutions for the projectable case of the covariant extension of Horava-Lifshitz Gravity, we show that an appropriate choice for the auxiliary field allows for an effective description of galaxy rotation curves. This description is based on static and spherically symmetric solutions of covariant Horava-Lifshitz Gravity and does not require Dark Matter.
In this paper we discuss the thermodynamics of the apparent horizon in $F(R)$ Hořava-Lifshitz gravity in equilibrium and non-equilibrium ensembles. We show that the second law of thermodynamics can be satisfied in this non relativistic theory.
We derive the projectable version of Horava - Lifshitz gravity from the localisation of the Galilean symmetry. Specifically we provide a dynamical construction of the metric, from first principles, that reproduces the transformations of the physical variables - lapse, shift and spatial component of the metric. Also, the measure defining the action is reproduced. The geometrical basis of the Horava-Lifshitz gravity is thereby revealed which also elucidates its difference from the Newton-Cartan geometry - the spacetime of Newtonian gravity. The connection of Newton's gravity with Horava-Lifshitz…
In this paper, we investigate the scalar quasinormal modes of Hořava-Lifshitz theory with $U(1)$ symmetry in static Anti-de Sitter spacetime. The static planar and spherical black hole solutions in lower energy limit are derived in non-projectable Hořava-Lifshitz gravity. The equation of motion of a scalar field is obtained, and is utilized to study the quasinormal modes of massless scalar particles. We find that the effect of Hořava-Lifshitz correction is to increase the quasinormal period as well as to slow down the decay of the oscillation magnitude. Besides, the scalar field could be unsta…
Horava-Lifshitz gravity with "detailed balance" but without the projectability assumption is discussed. It is shown that detailed balance is quite efficient in limiting the proliferation of couplings in Horava-Lifshitz gravity, and that its implementation without the projectability assumption leads to a theory with sensible dynamics. However, the (bare) cosmological constant is restricted to be large and negative.
We formulate Horava-Lifshitz cosmology with an additional scalar field that leads to an effective dark energy sector. We find that, due to the inherited features from the gravitational background, Horava-Lifshitz dark energy naturally presents very interesting behaviors, possessing a varying equation-of-state parameter, exhibiting phantom behavior and allowing for a realization of the phantom divide crossing. In addition, Horava-Lifshitz dark energy guarantees for a bounce at small scale factors and it may trigger the turnaround at large scale factors, leading naturally to cyclic cosmology.
We derive the detailed balance condition as a solution to the Hamilton-Jacobi equation in the Horava-Lifshitz gravity. This result leads us to propose the existence of the d-dimensional quantum field theory on the future boundary of the (d+1)-dimensional Horava-Lifshitz gravity from the viewpoint of the holographic renormalization group. We also obtain a Ricci flow equation of the boundary theory as the holographic RG flow, which is the Hamilton equation in the bulk gravity, by tuning parameters in the theory.
Slowly rotating black holes in the non-projectable Hořava-Lifshitz (HL) theory were studied recently in Phys. Rev. Lett. {\bf 109}, 181101 (2012), and claimed that they do not exist. In this Comment, we show that this is incorrect, and such solutions indeed exist in the IR limit of the non-projectable HL theory.
The z=3 deformed Horava-Lifshitz gravity with coupling constants ωand εleads to a nonrelativistic "mixmaster" cosmological model. The potential of theory is given by the sum of IR and UV potentials in the ADM Hamiltonian formalism. It turns out that the presence of the UV-potential cannot suppress chaotic behaviors existing in the IR-potential, which comes from curvature anisotropy.
We study the entropy of black holes in the deformed Horava-Lifshitz gravity with coupling constant lambda. For lambda=1, the black hole resembles the Reissner-Norstrom black hole with a geometric parameter acting like the electric charge. Therefore, we obtain some differences in the entropy when comparing with the Schwarzschild black hole. Finally, we study the heat capacity and the thermodynamical stability of this solution.
In this paper we continue the study of the Hamiltonian formalism of the healthy extended Horava-Lifshitz gravity. We find the constraint structure of given theory and argue that this is the theory with the second class constraints. Then we discuss physical consequence of this result. We also apply the Batalin-Tyutin formalism of the conversion of the system with the second class constraints to the system with the first class constraints to the case of the healthy extended Horava-Lifshitz theory. As a result we find new theory of gravity with structure that is different from the standard formul…
Causal Dynamical Triangulations (CDT) is a lattice theory where aspects of quantum gravity can be studied. Two-dimensional CDT can be solved analytically and the continuum (quantum) Hamiltonian obtained. In this article we show that this continuum Hamiltonian is the one obtained by quantizing two-dimensional projectable Horava-Lifshitz gravity.
In this short note we clarify a link between anisotropic-scaling scenarios and Finsler spacetimes. Generalizing earlier analysis it is shown that the kinematics of propagating particles (in the sense of geometrical optics) can be described in terms of (pseudo-)Finsler structures.
We discuss some aspects of the Horava-Lifshitz cosmology with different matter components considered as dominants at different stages of the cosmic evolution (each stage is represented by an equation of state pressure/density=constant). We compare cosmological solutions from this theory with their counterparts of General Relativity (Friedmann cosmology). At early times, the Horava- Lifshitz cosmology contains a curvature-dependent dominant term which is stiff matter-reminiscent and this fact motivates to discuss, in some detail, this term beside the usual stiff matter component (pressure=densi…
Non-stationary null dust in a spherically symmetric spacetime is studied in the context of a general-covariant Horava-Lifshitz theory. The non-minimal coupling to matter is considered in the infrared limit. The aim of this paper is to study whether the collapse of a null dust-like fluid can be a solution of Hořava-Lifshitz theory in the infrared limit. We have shown that the unique possible solution is static. This solution represents a Minkowski spacetime since the energy density is null.
In this paper we investigate the physical implications of the dynamical scalar mode in pure Horava-Lifshitz gravity on cosmology. We find that it can produce a scale-invariant power spectrum in UV era if the detailed balance condition on the action is relaxed. This indicates that the physical scalar mode may seed the large scale structure and Horava-Lifshitz cosmology could be a qualified alternative to inflationary scenario.
We use the Wetterich equation for foliated spacetimes to study the RG flow of projectable Horava-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 RG 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 Horava-Lifshitz gravity is perturbatively renormalizabl…
We quantize the two-dimensional projectable Horava-Lifshitz gravity with a bi-local as well as space-like wormhole interaction. The resulting quantum Hamiltonian coincides with the one obtained through summing over all genus in the string field theory for two-dimensional causal dynamical triangulations. This implies that our wormhole interaction can be interpreted as a splitting or joining interaction of one-dimensional strings.
In this letter, we have considered generalized Ricci dark energy in the Horava-Lifshitz gravity. We have reconstructed the Hubble's parameter in terms of fractional densities. We have viewed the equation of state parameter in this situation. Also, we have examined the behavior of deceleration parameter and investigated the nature of the statefinder diagnostics. The equation of state parameter has exhibited quintessence-like behavior and from the plot of the deceleration parameter we have observed an ever accelerating universe.
We investigate the connection between Gravity's Rainbow and Horava-Lifshitz gravity, since both theories incorporate a modification in the UltraViolet regime which improves their quantum behavior at the cost of the Lorentz invariance loss. In particular, extracting the Wheeler-De Witt equations of the two theories in the case of Friedmann-Lemaitre-Robertson-Walker and spherically symmetric geometries, we establish a correspondence that bridges them.
We show that certain three-dimensional Horava-Lifshitz gravity theories can be written as Chern-Simons gauge theories on various non-relativistic algebras. The algebras are specific extensions of the Bargmann, Newton-Hooke and Schroedinger algebra each of which has the Galilean algebra as a subalgebra. To show this we employ the fact that Horava-Lifshitz gravity corresponds to dynamical Newton-Cartan geometry. In particular, the extended Bargmann (Newton-Hooke) Chern-Simons theory corresponds to projectable Horava-Lifshitz gravity with a local U(1) gauge symmetry without (with) a cosmological …
Analytical solutions of Maxwell equations around black hole immersed in external uniform magnetic field in the background of the Kehagias-Sfetsos (KS) asymptotically flat black hole solution of Hořava-Lifshitz gravity have been found. Influence of magnetic field on effective potential of the radial motion of charged test particle around black hole immersed in external magnetic field in Hořava-Lifshitz gravity has been investigated by using Hamilton-Jacobi method. Exact analytical solution for dependence of the minimal radius of the circular orbits $r_{\rm mc}$ from KS parameter $ω$ for motion …
We find topological (charged) black holes whose horizon has an arbitrary constant scalar curvature $2k$ in Hořava-Lifshitz theory. Without loss of generality, one may take $k=1,0$ and -1. The black hole solution is asymptotically AdS with a nonstandard asymptotic behavior. Using the Hamiltonian approach, we define a finite mass associated with the solution. We discuss the thermodynamics of the topological black holes and find that the black hole entropy has a logarithmic term in addition to an area term. We find a duality in Hawking temperature between topological black holes in Hořava-Lifshit…
In the present paper we consider the possibility of observationally testing Horava gravity at the scale of the Solar System, by considering the classical tests of general relativity (perihelion precession of the planet Mercury, deflection of light by the Sun and the radar echo delay) for the Kehagias-Sfetsos asymptotically flat black hole solution of Horava-Lifshitz gravity. All these gravitational effects can be fully explained in the framework of the vacuum solution of Horava gravity, and it is shown that the analysis of the classical general relativistic tests severely constrain the free pa…
Approximately one year ago Horava proposed a power-counting renormalizable theory of gravity which abandons local Lorentz invariance. The proposal has been received with growing interest and resulted in various different versions of Horava-Lifshitz gravity theories, involving a colourful potpourri of new terminology. In this proceedings contribution we first motivate and briefly overview the various different approaches, clarifying their differences and similarities. We then focus on a model referred to as projectable Horava-Lifshitz gravity and summarize the key results regarding its viabilit…
We investigate the propagation and evolution for a massless scalar field in the background of $λ=1/2$ Hořava-Lifshitz black hole with the condition of detailed balance. We fortunately obtain an exact solution for the Klein-Gordon equation. Then, we find an analytical expression for the greybody factor which is valid for any frequency; and also exactly show that the perturbation decays without any oscillation. All of these can help us to understand more about the Hořava-Lifshitz gravity.
We investigate slowly rotating black holes in the Hořava-Lifshitz (HL) gravity. For $Λ_W=0$ and $λ=1$, we find a slowly rotating black hole of the Kehagias-Sfetsos solution in asymptotically flat spacetimes. We discuss their thermodynamic properties by computing mass, temperature, angular momentum, and angular velocity on the horizon.
We consider the electrostatic field of a point charge coupled to Horava-Lifshitz gravity and find an exact solution describing the space with a surplus (or deficit) solid angle. Although, theoretically in general relativity, a surplus angle is hardly to be obtained in the presence of ordinary matter with positive energy distribution, it seems natural in Horava-Lifshitz gravity. We present the sudden disappearance and reappearance of a star image as an astrophysical effect of a surplus angle. We also consider matter configurations of all possible power law behaviors coupled to Horava-Lifshitz g…
We investigate the Hamiltonian structure of linearized extended Hořava- Lifshitz gravity in a flat cosmological background following the Faddeev-Jackiw's Hamiltonian reduction formalism. The Hamiltonian structure of extended Hořava-Lifshitz gravity is similar to that of the projectable version of original Hořava-Lifshitz gravity, in which there is one primary constraint and so there are two physical degrees of freedom. We also find that extra scalar graviton mode in an inflationary background can be decoupled from the matter field in the infrared (IR) limit, but it is coupled to the matter fie…
We look for a Brans-Dicke type of generalization of the Horava-Lifshitz gravity. It is shown that such a generalization is possible within the detailed balance condition. Classically, the resulting theory reduces in the IR limit to the usual Brans-Dicke theory with a negative cosmological constant for certain values of parameters. We then consider homogeneous and isotropic cosmology and study the effects of the new terms appearing in the model.
In this paper we show that by considering a slightly modified Horava-Lifshitz gravity one can find self-tuning cosmological scenarios. Since in the proposed model the cosmological constant cancels out, then regardless of its value it cannot produce any gravitational effect. As a consequence this removes the gravitational effect of the vacuum energy on the expansion of the Universe. Accelerating scenarios, however, can be found through the presence of conventional and non-conventional fluids.
In this paper we focus on the Halmiton-Jacobi method to determine several thermodynamic quantities such as the temperature, entropy and specific heat of two-dimensional Horava-Lifshitz black holes by using the generalized uncertainty principles (GUP). We also address the product of horizons, mainly concerning the event, Cauchy, cosmological and virtual horizons.
We study linear cosmological perturbations in the ``healthy extension'' of Horava-Lifshitz gravity which has recently been analyzed \cite{BPS2}. We find that there are two degrees of freedom for scalar metric fluctuations, but that one of them decouples in the infrared limit. Also, for appropriate choices of the parameters defining the Lagrangian, the extra mode can be made well-behaved even in the ultraviolet.
The anti--de Sitter/conformal field theory (AdS/CFT) correspondence is a powerful tool that promises to provide new insights toward a full understanding of field theories under extreme conditions, including but not limited to quark-gluon plasma, Fermi liquid and superconductor. In many such applications, one typically models the field theory with asymptotically AdS black holes. These black holes are subjected to stringy effects that might render them unstable. Hořava-Lifshitz gravity, in which space and time undergo different transformations, has attracted attentions due to its power-counting …
The occurrence of a bounce in the FRW cosmology requires modifications of General Relativity. An example of such a modification is the recently proposed Horava-Lifshitz theory of gravity, which includes a "dark radiation" term with a negative coefficient in the analog of the Friedmann equation. A modification of the HL gravity, relaxing the "detailed balance" condition, brings additional terms to the equations of motion, corresponding to stiff matter. This paper presents comparison of the phase structure of the original and modified Horava cosmology. Special attention is paid to the analysis o…
We perform the phase space analysis in terms of the linearization technique in the Hořava-Lifshitz gravity with the softly broken detailed balance condition. It can be shown that the bouncing universe appears only for the positive spatial curvature of $k=+1$, and it is possible to obtain oscillating universe with the help of the negative dark radiation and the negative cosmological constant.
We perform a detailed phase-space analysis of Horava-Lifshitz cosmology, with and without the detailed-balance condition. Under detailed-balance we find that the universe can reach a bouncing-oscillatory state at late times, in which dark-energy, behaving as a simple cosmological constant, is dominant. In the case where the detailed-balance condition is relaxed, we find that the universe reaches an eternally expanding, dark-energy-dominated solution, with the oscillatory state preserving also a small probability. Although this analysis indicates that Horava-Lifshitz cosmology can be compatible…
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 $λ$ of the theory.
An extension of Horava-Lifshitz gravity was recently proposed in order to address the pathological behavior of the scalar mode all previous versions of the theory exhibit. We show that even in this new extension the strong coupling persists, casting doubts on whether such a model can constitute an interesting alternative to general relativity (GR).
Constraints on Covariant Horava-Lifshitz Gravity from precision measurement of planetary gravitomagnetic field
本文分析了 Horava-Lifshitz 修正对引力磁场的影响，提出了一种基于星载激光干涉测量的行星引力磁场测量方法来约束该理论参数，发现高精度激光梯度计可将约束结果改善一到两个数量级。
The stability of de Sitter spacetime in Horava-Lifshitz theory of gravity with projectability but without detailed balance condition is studied. It is found that, in contrast to the case of the Minkowski background, the spin-0 graviton now is stable for any given $ξ$, and free of ghost for $ξ\le 0$ in the infrared limit, where $ξ$ is the dynamical coupling constant.
We perform a fully nonlinear analysis of superhorizon perturbation in Hořava-Lifshitz gravity, based on the gradient expansion method. We present a concrete expression for the solution of gravity equations up to the second order in the gradient expansion, and prove that the solution can be extended to any order. The result provides yet another example for analogue of the Vainshtein effect: the nonlinear solution is regular in the limit $λ\to 1$ and recovers general relativity coupled to dark matter at low energy. Finally, we propose a definition of nonlinear curvature perturbation ${\cal R}$ i…
We consider linear perturbations about a homogeneous and isotropic cosmological background in the projectable version of Hořava-Lifshitz gravity. Starting from the action for cosmological perturbations, we identify the canonically normalized fluctuation variables. We find that - in contrast to what happens in the non-projectable version of the theory - the extra scalar cosmological perturbation mode is already dynamical at the level of linear perturbations. For values of the parameter $λ$ in the range $1/3 < λ< 1$, the extra mode is ghost-like, for values $1 < λ$ and $λ< 1/3$ it is tachyonic. …
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