Horava-Lifshitz Research Articles

Primordial dust universe in the Hořava–Lifshitz theory

In this paper, we apply quantum cosmology to investigate the early moments of a Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model, using Hořava–Lifshitz (HL) as the gravitational theory. The matter content of the model is a dust perfect fluid. We start studying the classical model. Then, we write the total Hamiltonian of the model, quantize it and find the appropriate Wheeler–DeWitt equation. In order to avoid factor ordering ambiguities, in the Wheeler–DeWitt equation, we introduce a canonical transformation. We solve that equation using the Wentzel–Kramers–Brillouin (WKB) approximation and compute the tunneling probabilities for the birth of that universe ([Formula: see text]). Since the WKB wave function depends on the dust energy and the free coupling constants coming from the HL theory, we compute the behavior of [Formula: see text] as a function of all these quantities.

Thermodynamic topology of D = 4,5 Horava Lifshitz black hole in two ensembles

In this paper, we investigate the thermodynamic topology of four and five-dimensional Hořava-Lifshitz (HL) black holes within Hořava gravity. To analyze their thermodynamic topology, we treat these HL black holes as topological defects in their thermodynamic spaces and compute the winding numbers at these defects. Our study is conducted in two different ensembles: the fixed ϵ ensemble and the fixed ζ ensemble, where ϵ is a parameter of the HL black holes, and ζ is its conjugate parameter. In the fixed ϵ ensemble, we consider three different horizon types: spherical (k=+1), flat (k=0), and hyperbolic (k=−1), while in the fixed ζ ensemble, we examine two horizon types: spherical (k=+1) and hyperbolic (k=−1). For all the aforementioned cases, we study the local and global topology of these black holes and classify them into topological classes based on their topological charges. We calculate the topological number for each case. This process uncovers some novel phase diagrams that reveal a number of multiple defect curve phenomenon. Additionally, we explore how the topological charge of these black holes depends on the values of the thermodynamic parameters. Our findings indicate that the thermodynamic topology of Hořava-Lifshitz black holes in D=4,5 is significantly influenced by the type of horizon, the choice of ensemble, the values of pressure, and the parameters ϵ or ζ.

Observational Constraints on the Parameters of Hořava–Lifshitz Gravity

AbstractThis study investigates the accelerated cosmic expansion within the Hořava–Lifshitz (HL) Model. To constrain the cosmological parameters of this model, 17 Baryon Acoustic Oscillation points, 31 Cosmic Chronometer points, 40 Type Ia Supernovae points, 24 quasar Hubble diagram points, and 162 Gamma Ray Bursts points, along with the latest Hubble constant measurement (R22) are incorporated. is treated as a free parameter to extract and using late‐time datasets, aiming for optimal fitting values in each model. Treating as free improves precision, reduces bias, and enhances dataset compatibility. The obtained values of and are compared to the model, showing consistency with previous estimates from Planck and SDSS studies. The Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) favor the Hořava–Lifshitz model, with the model having the lowest AIC. Additionally, and analyses are conducted to assess model preference. Validation using the reduced statistic indicates satisfactory fits for the Hořava–Lifshitz model, while recognizing as the preferred model. Extensions of the analysis warrant further investigation.

Cosmological test of dark energy parameterizations in Hořava–Lifshitz gravity

In this work, we assume that the FLRW universe, which is filled with dark matter along with dark energy, is in the framework of Hořava–Lifshitz (HL) gravity. The dark energy is considered as the linear (Model I) and CPL (Model II) parameterizations of the equation of state parameter. For both models, we express the Hubble parameter H(z) in terms of the model parameters and redshift z. To rigorously constrain the model, we have employed a comprehensive set of recent observational datasets, including cosmic chronometers (CC), type Ia supernovae (SNIa), baryon acoustic oscillations (BAO), gamma-ray burst (GRB), quasar (Q) and cosmic microwave background radiation (CMB). Through the joint analysis of this diverse collection of datasets, we have achieved tighter constraints on the model’s parameters. This, in turn, allows us to delve into both the physical and geometric aspects of the model with greater precision. Furthermore, our analysis has enabled us to determine the present values of crucial cosmological parameters, including H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_{0}$$\\end{document}, Ωm0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _{m0}$$\\end{document}, Ωk0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _{k0}$$\\end{document} and ΩΛ0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _{\\Lambda 0}$$\\end{document}. It is noteworthy that our results are consistent with recent findings from Planck 2018, underscoring the reliability and relevance of our models in the current cosmological context. We also conduct analysis of cosmographic parameters and apply statefinder and diagnostic tests to explore the evolution of the Universe. In addition, the statistical analysis suggests that the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model is the preferred model among all our considered models. Our investigation into the models has unveiled intriguing features of the late Universe.

Thermodynamical phase transitions of AdS black hole in Horava–Lifshitz gravity

In this paper, we investigate the thermodynamical phase transitions of the spherically symmetric AdS black hole in Horava–Lifshitz (HL) gravity for the detailed balance violation parameter [Formula: see text]. First, by calculating the HP temperature [Formula: see text], the minimum temperature [Formula: see text] and the Gibbs free energy [Formula: see text] of the AdS black hole in different values of parameter [Formula: see text], we find that the HP phase transition can occur at all pressures. Comparing the HP temperature [Formula: see text] with the minimum temperature [Formula: see text], we notice that the ratio of [Formula: see text] tends to 1 when [Formula: see text]. Second, for the small–large black hole phase transition of the AdS black hole, we discover that the black hole heat capacity is divergent at the minimum temperature [Formula: see text], the small–large black hole phase transition occurs at the same time. Furthermore, the black hole entropy also exists [Formula: see text] when [Formula: see text], and [Formula: see text] when the black hole temperature has its minimum [Formula: see text], we surprisingly find that the ratio of [Formula: see text] tends to [Formula: see text] when the dimension [Formula: see text], which provides a general relation between the Hawking–Page phase transition and the small–large black hole phase transition of the AdS black hole in the large dimension. All in all, the ratios of typical temperature and entropy of two kinds of phase transitions tend to natural constant in the large dimension limit, which may imply to understand the nature of two different phase transitions.

Probing Hořava-Lifshitz gravity using particle and photon dynamics in the presence of plasma* *This study is partly supported by Grants F-FA-2021-432, F-FA-2021-510, and MRB-2021-527 of the Ministry of Higher Education, Science and Innovations of the Republic of Uzbekistan

We study the particle motion around a black hole (BH) in Hořava-Lifshitz (HL) gravity with the Kehagias-Sfetsos (KS) parameter. First, the innermost stable circular orbit (ISCO) is obtained for massive particles around the BH in HL gravity. We find that the radii of the ISCOs decrease as the KS parameter decreases, meaning that the parameter causes the orbits of particles to move inward with respect to that of the Schwarzschild BH case. Then, the optical properties of a KS BH are studied in detail, that is, the BH shadow and gravitational weak lensing. We demonstrate that the size of the BH shadow decreases under the influence of the KS parameter.

Resolution of Cosmological Singularity in Hořava–Lifshitz Cosmology

The standard ΛCDM model, despite its agreement with observational data, still has some issues unaddressed, such as the problem of initial singularity. Solving that problem usually requires modifications of general relativity. However, there appeared the Hořava–Lifshitz (HL) theory of gravity, in which equations governing cosmological evolution include a new term scaling similarly as the dark radiation term in the Friedmann equations, enabling a bounce of the universe instead of initial singularity. This review describes past works on the stability of such a bounce in different formulations of HL theory, an initial detailed balance scenario, and further projectable versions containing higher than quadratic terms to the original action.

The Horava–Lifshitz modifications of the Casimir effect at finite temperature revisited

We investigate the Casimir force for parallel plates at finite temperature in the Horava–Lifshitz (HL) theory. We find that the HL exponent cannot be chosen as an integer, or the Casimir energy will be a constant, and further, the Casimir force between two parallel plates will vanish. The higher temperature causes the attractive Casimir force to weaken, which is consistent with the original results confirmed theoretically and experimentally. We can select the HL factor appropriately to obtain a thermally revised Casimir force similar to the standard results for the parallel plates.

DeWitt wave function in Hořava-Lifshitz cosmology with tensor perturbation

We present a well-tempered DeWitt wave function, which vanishes at the classical big-bang singularity, in Hořava-Lifshitz (HL) cosmology with tensor perturbation, both analytically and numerically. In general relativity, the DeWitt wave function is ill-behaved once the tensor perturbation is taken into account. This is essential because the amplitude of the perturbation diverges at the singularity and the perturbative expansion completely breaks down. On the other hand, in HL gravity it is known that the higher dimensional operators required by the perturbative renormalizability render the tensor perturbation scale-invariant and regular all the way up to the singularity. In this paper we analytically show that in d+1 dimensional HL gravity, the DeWitt wave function for tensor perturbation is indeed well-defined around the classical big-bang singularity. Also, we numerically demonstrate the well-behaved DeWitt wave function for tensor perturbation from the singularity to the finite size of the Universe.

Chaos in spatially homogeneous Hořava–Lifshitz subcritical cosmologies

We consider spatially homogeneous models in Hořava–Lifshitz (HL) gravity that perturbs general relativity (GR) by a parameter v ∈ (0, 1) such that GR occurs at v = 1/2. We prove that the induced Kasner map is chaotic for a broad class of modified HL gravity models, when v ∈ (0, 1/2), despite the fact that the Kasner map is multi-valued in such subcritical regime.

Shadows and rings of the Kehagias-Sfetsos black hole surrounded by thin disk accretion

In this paper, under the illumination of thin disk accretion, we have employed the ray-tracing method to carefully investigate shadows and rings of the Kehagias-Sfetsos(KS) black hole in deformed Hořava-Lifshitz(HL) gravity.The results show that the event horizon r+, the radius r_p and impact parameter bp of photon sphere are all decreased with the increase of the HL parameter ω, but the effective potential increases. And, it also turns out that the trajectories of light rays emitted from the north pole direction are defined as the direct emission, lensing ring and photon ring of KS black hole, on the basis of orbits n = ϕ/2π.As black hole surrounded by thin disk accretion, we show that the corresponding transfer functions have their values increased with the parameter ω. More importantly, we also find that the direct emissions always dominate the total observed intensity, while lensing rings as a thin ring make a very small contribution and photon ring as a extremely narrow ring make a negligible contribution, for all three toy-model functions. In view of this, the results finally imply that shadows and rings as the observational appearance of KS black hole exhibit some obvious interesting features, which might be regarded as an effective way to distinguish black holes in HL gravity from the Schwarzschild black hole.

Quantum creation of a toy Universe without inflation

We propose a toy model for the origin of the Universe, where the scale-invariant fluctuations are generated together with the quantum creation process of the Universe. The fluctuations arise inside an instanton in the Euclidean domain of time. In the Lorentzian point of view, the Universe emerges with passive, coherent and scale-invariant fluctuations present from the beginning, without the need of inflation or a bounce. For this mechanism to work, we need anisotropic scaling in space and time, which is realized in a toy model of Horava–Lifshitz (HL) gravity with a Lifshitz scalar field.

Black hole evaporation in Ho\u0159ava\u2013Lifshitz gravity

Hořava–Lifshitz (HL) gravity was formulated in hope of solving the non-renormalization problem in Einstein gravity and the ghost problem in higher derivative gravity theories by violating Lorentz invariance. In this work we consider the spherically symmetric neutral AdS black hole evaporation process in HL gravity in various spacetime dimensions d, and with detailed balance violation parameter 0leqslant epsilon ^2leqslant 1. We find that the lifetime of the black holes under Hawking evaporation is dimensional dependent, with d=4,5 behave differently from dgeqslant 6. For the case of epsilon =0, in d=4,5, the black hole admits zero temperature state, and the lifetime of the black hole is always infinite. This phenomenon obeys the third law of black hole thermodynamics, and implies that the black holes become an effective remnant towards the end of the evaporation. As dgeqslant 6, however, the lifetime of black hole does not diverge with any initial black hole mass, and it is bounded by a time of the order of ell ^{d-1}, similar to the case of Schwarzschild-AdS in Einstein gravity (which corresponds to epsilon ^2=1), though for the latter this holds for all dgeqslant 4. The case of 0<epsilon ^2<1 is also qualitatively similar with epsilon =0.

Composite Nambu–Jona-Lasinio inflation near infrared fixed point of the Hořava-Lifshitz theory

In this work, we first propose a cosmological scenario inherently based on the effective Nambu–Jona-Lasio (NJL) model near the infrared (IR) limit of the Hořava-Lifshitz (HL) theory. Having used the one-loop correction, we employ the NJL framework in the ultraviolet (UV) limit of the HL theory, with critical exponent z=3, to demonstrate in the IR limit that the symmetry of the potential at the critical coupling value is broken at z=1. We also derive the effective Higgs-like potential in the low energy regimes. Here the symmetry of the effective potential will be broken near z=1 at a certain value of the critical coupling. In our scenario, the scalar channel of the NJL model plays the role of a composite inflaton. We find that the Lorentz invariance (LI) appears at the IR regime of the HL theory and employ the standard inflationary (slow-roll) paradigm as a probe of physics at very high energy. We compute inflationary parameters and compare them with recent Planck 2015 data. Interestingly, we discover that the predictions of the model are in perfect agreement with the Planck analysis. Our salient feature is that we used inflation to quantify the IR and UV fixed points of underlying theory. We discover that the IR fixed point of HL gravity is compatible with the grand unified energy scale; whilst the UV fixed point is the Planck energy scale.

Tunnelling radiation of charged particles from a Hořava–Lifshitz gravity black hole

The Hawking radiation of charged particles from black holes in the Hořava–Lifshitz (HL) gravity is investigated by using the Parikh–Wilczek (PW) method, and the emission rate is calculated. The emission spectrum is not purely thermal and is consistent with an underlying unitary theory. Some other characteristics exist for a HL gravity black hole. Assuming the conventional tunnelling rate associated with the change of entropy, the entropy of the HL gravity black hole is obtained. The entropy is not proportional to the horizon area because a logarithmic term exists. However, it complies with the first law of thermodynamics and is in accord with earlier results.

Inflationary perturbations with Lifshitz scaling

Instead of Lorentz invariance, gravitational degrees of freedom may obey Lifshitz scaling at high energies, as it happens in Hořava's proposal for quantum gravity. We study consequences of this proposal for the spectra of primordial perturbations generated at inflation. Breaking of 4D diffeomorphism (Diff) invariance down to the foliation-preserving Diff in Hořava-Lifshitz (HL) gravity leads to appearance of a scalar degree of freedom in the gravity sector, khronon, which describes dynamics of the time foliation. One can naively expect that mixing between inflaton and khronon will jeopardize conservation of adiabatic perturbations at super Hubble scales. This indeed happens in the projectable version of the theory. By contrast, we find that in the non-projectable version of HL gravity, khronon acquires an effective mass which is much larger than the Hubble scale well before the Hubble crossing time and decouples from the adiabatic curvature perturbation ζ sourced by the inflaton fluctuations. As a result, at super Hubble scales the adiabatic perturbation ζ behaves as in an effectively single field system and its spectrum is conserved in time. Lifshitz scaling is imprinted in the power spectrum of ζ through the modified dispersion relation of the inflaton. We point out violation of the consistency relation between the tensor-to-scalar ratio and the spectral tilt of primordial gravitational waves and suggest that it can provide a signal of Lorentz violation in inflationary era.

Revisit on the thermodynamic stability of Hořava–Lifshitz black hole

We study the thermodynamic properties of the black hole derived in Hořava–Lifshitz (HL) gravity without the detailed-balance condition. The parameter [Formula: see text] in the HL black hole plays the same role as that of the electric charge in the Reissner–Nordström-anti-de Sitter (RN-AdS) black hole. By analogy, we treat the parameter [Formula: see text] as the thermodynamic variable and obtain the first law of thermodynamics for the HL black hole. Although the HL black hole and the RN-AdS black hole have the similar mass and temperature, due to their very different entropy, the two black holes have very different thermodynamic properties. By calculating the heat capacity and the free energy, we analyze the thermodynamic stability of the HL black hole.

Quantum to classical transition in the Hořava-Lifshitz quantum cosmology

A quasi-Gaussian quantum superposition of Hořava-Lifshitz (HL) stationary states is built in order to describe the transition of the quantum cosmological problem to the related classical dynamics. The obtained HL phase-space superposed Wigner function and its associated Wigner currents describe the conditions for the matching between classical and quantum phase-space trajectories. The matching quantum superposition parameter is associated to the total energy of the classical trajectory which, at the same time, drives the engendered Wigner function to the classical stationary regime. Through the analysis of the Wigner flows, the quantum fluctuations that distort the classical regime can be quantified as a measure of (non)classicality. Finally, the modifications to the Wigner currents due to the inclusion of perturbative potentials are computed in the HL quantum cosmological context. In particular, the inclusion of a cosmological constant provides complementary information that allows for connecting the age of the Universe with the overall stiff matter density profile.

Phase transition and holographic in modified Horava–Lifshitz black hole

In this paper, we take cosmological constant as a thermodynamical pressure and its conjugate quantity as a thermodynamical volume. This expression helps us to investigate the phase transition and holographic heat engine. So, in order to have Van der Waals fluid behavior in Horava–Lifshitz (HL) black hole, we modified the solution of such black hole with some cosmology ansatz. Also from holographic heat engine, we obtain Carnot efficiency for the HL black hole. The phase transition of the system lead us to investigate the stability condition for the corresponding black hole. In that case, we show that the stability exist only in special region of black hole.

Phase transition and thermodynamic stability of topological black holes in Hořava–Lifshitz gravity

On the basis of horizon thermodynamics, we study the thermodynamic stability and criticality of topological black holes constructed in Hořava–Lifshitz (HL) gravity without the detailed-balance condition (with general ϵ). In the framework of horizon thermodynamics, we do not need the concrete black hole solution (the metric function) and the concrete matter fields. It is shown that the HL black hole for is always thermodynamically stable. For , the thermodynamic behaviors and criticality of the HL black hole are similar to those of RN-AdS black hole for some . For , the temperature is classified into six types by their different features. Among them, we mainly focus on the type with a triply degenerate thermodynamic state. It is also shown that there is a ‘thermodynamic singularity’ for the HL black hole, where the temperature and Gibbs free energy both diverge apart from a special pressure Ps.