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1.
Inspired by Lifshitz theory for quantum critical phenomena in condensed matter, Horava proposed a theory for quantum gravity with an anisotropic scaling in ultraviolet. In Horava-Lifshitz gravity (HLG), we have studied the impacts of six types of equations of state on the evolution of various cosmological parameters such as Hubble parameters and scale factor. From the comparison of the general relativity gravity with the HLG with detailed and without with non-detailed balance conditions, remarkable differences are found. Also, a noticeable dependence of singular and non-singular Big Bang on the equations of state is observed. We conclude that HLG explains various epochs in the early universe and might be able to reproduce the entire cosmic history with and without singular Big Bang. 相似文献
2.
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 Horava-Lifshitz gravity in retaining only spatial diffeomorphisms (instead of full space-time covariance) as the physically relevant non-trivial gauge symmetry; at the same time the local Hamiltonian constraint needed to eliminate the extra mode is equivalently enforced by the master constraint. 相似文献
3.
We build holographic p-wave conductor(insulator)/superconductor models via the numerical method with a new form of Weyl coupling in five-dimensional Lifshitz gravity, and then investigate how the Weyl coupling parameter γ and the Lifshitz scaling parameter z affect the superconductor models.In the conductor/superconductor model, an increase in the Weyl correction(Lifshitz scaling)enhances(inhibits) the superconductor phase transition. Meanwhile, both the Weyl correction(when the Lifshitz parameter is large enough and fixed) and the Lifshitz scaling suppress the growth of the real part of the conductivity. The Weyl correction used here(CB~2) shows weaker effects on the critical value than the previous Weyl correction(CF~2). In the insulator/superconductor model, larger vaules of the Weyl parameter hinder the formation of condensate. However, in increase in the Lifshitz scaling enhances the appearance of condensate. In addition, the calculation suggests that a competitive relation may exist between the Weyl correction and the Lifshitz scaling. 相似文献
4.
For charged black holes in Ho?ava–Lifshitz gravity, a second order phase transition takes place in extended phase space where the cosmological constant is taken as thermodynamic pressure. We relate the second order nature of phase transition to the fact that the phase transition occurs at a sharp temperature and not over a temperature interval. Once we know the continuity of the first derivatives of the Gibbs free energy, we show that all the Ehrenfest equations are readily satisfied. We study the effect of the perturbation of the cosmological constant as well as the perturbation of the electric charge on thermodynamic stability of Ho?ava–Lifshitz black hole. We also use thermodynamic geometry to study phase transition in extended phase space. We investigate the behavior of scalar curvature of Weinhold, Ruppeiner, and Quevedo metric in extended phase space of charged Ho?ava–Lifshitz black holes. It is checked if these curvatures could reproduce the result of specific heat for the phase transition. 相似文献
5.
In this paper, we will incorporate the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bosonic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporate the generalized uncertainty principle into a non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations. We will also perform the stochastic quantization of this Lifshitz fermionic theory based generalized uncertainty principle. 相似文献
6.
We investigate the Hamiltonian structure of linearized extended Ho?ava–Lifshitz gravity in a flat cosmological background following the Faddeev–Jackiw's Hamiltonian reduction formalism. The Hamiltonian structure of extended Ho?ava–Lifshitz gravity is similar to that of the projectable version of original Ho?ava–Lifshitz gravity, in which there is one primary constraint and so there are two physical degrees of freedom. In the infrared (IR) limit, however, there is one propagating degree of freedom in the general cosmological background, and that is coupled to the scalar graviton mode. We find that extra scalar graviton mode in an inflationary background can be decoupled from the matter field in the IR limit. But it is necessary to go beyond linear order in order to draw any conclusion of the strong coupling problem. 相似文献
7.
We calculate the susceptibility amplitude ratio near a generic higher character Lifshitz point up to one-loop order. We employ a renormalization group treatment with L independent scaling transformations associated to the various inequivalent subspaces in the anisotropic case in order to compute the ratio above and below the critical temperature and demonstrate its universality. Furthermore, the isotropic results with only one type of competition axes have also been shown to be universal. We describe how the simpler situations of m-axial Lifshitz points as well as ordinary (noncompeting) systems can be retrieved from the present framework. 相似文献
8.
Masud Chaichian Markku Oksanen Anca Tureanu 《The European Physical Journal C - Particles and Fields》2011,71(6):1657
We study the recently proposed Covariant Renormalizable Gravity (CRG), which aims to provide a generally covariant ultraviolet
completion of general relativity. We obtain a spacetime decomposed form—an Arnowitt–Deser–Misner (ADM) representation—of the
CRG action. The action is found to contain time derivatives of the gravitational fields up to fourth order. Some ways to reduce
the order of these time derivatives are considered. The resulting action is analyzed using the Hamiltonian formalism, which
was originally adapted for constrained theories by Dirac. It is shown that the theory has a consistent set of constraints.
It is, however, found that the theory exhibits four propagating physical degrees of freedom. This is one degree of freedom
more than in Hořava–Lifshitz (HL) gravity and two more propagating modes than in general relativity. One extra physical degree
of freedom has its origin in the higher order nature of the CRG action. The other extra propagating mode is a consequence
of a projectability condition similarly as in HL gravity. Some additional gauge symmetry may need to be introduced in order
to get rid of the extra gravitational degrees of freedom. 相似文献
9.
We compute the axial anomaly of a Lifshitz fermion theory with anisotropic scaling z = 3 which is minimally coupled to geometry in 3+1 space‐time dimensions. We find that the result is identical to the relativistic case using path integral methods. An independent verification is provided by showing with spectral methods that the η‐invariant of the Dirac and Lifshitz fermion operators in three dimensions are equal. Thus, by the integrated form of the anomaly, the index of the Dirac operator still accounts for the possible breakdown of chiral symmetry in non‐relativistic theories of gravity. We apply this framework to the recently constructed gravitational instanton backgrounds of Hořava–Lifshitz theory and find that the index is non‐zero provided that the space‐time foliation admits leaves with harmonic spinors. Using Hitchin's construction of harmonic spinors on Berger spheres, we obtain explicit results for the index of the fermion operator on all such gravitational instanton backgrounds with SU(2) × U(1) isometry. In contrast to the instantons of Einstein gravity, chiral symmetry breaking becomes possible in the unimodular phase of Hořava–Lifshitz theory arising at λ = 1/3 provided that the volume of space is bounded from below by the ratio of the Ricci to Cotton tensor couplings raised to the third power. Some other aspects of the anomalies in non‐relativistic quantum field theories are also discussed. 相似文献
10.
We investigate the Lifshitz black holes from the Ho?ava–Lifshitz gravity by comparing with the Lifshitz black hole from the 3D new massive gravity. We note that these solutions all have single horizons. These black holes are very similar to each other when studying their thermodynamics. It is shown that a second order phase transition is unlikely possible to occur between z=3,2 Lifshitz black holes and z=1 Ho?ava black hole. 相似文献
11.
I. Bakas 《Fortschritte der Physik》2012,60(3):224-242
We show that the gauge and metric field contribution to the axial anomaly of a four‐dimensional massless Lifshitz fermion theory with anisotropy scaling exponent z is identical to the relativistic case, hereby extending the results found in arXiv:1103.5693 to arbitrary values of z. This is in accordance with the fact that the axial anomaly is an infra‐red phenomenon in disguise. We also provide some new models that realize baryon and lepton number violation in non‐relativistic theories of gravity. In all cases, the volume of space exhibits a lower bound that is fixed by the gravitational coupling parameters. 相似文献
12.
Yun Soo Myung Yong-Wan Kim Young-Jai Park 《The European Physical Journal C - Particles and Fields》2010,70(1-2):335-340
The z=3 Lifshitz black hole is an exact black hole solution to the new massive gravity in three dimensions. In order to understand this black hole clearly, we perform a dimensional reduction to two-dimensional dilaton gravity by utilizing the circular symmetry. Considering the linear dilaton, we find the same Lifshitz black hole in two dimensions. This implies that all thermodynamic quantities of the z=3 Lifshitz black hole could be obtained from its corresponding black hole in two dimensions. As a result, we derive the temperature, mass, heat capacity, Bekenstein–Hawking entropy, and free energy. 相似文献
13.
Recently a renormalizable model of gravity has been proposed, which might be a UV completion of General Relativity (GR) or its infra-red modification, probably with a strongly coupled scalar mode. Although the generic vacuum of the theory is anti-de Sitter one, particular limits of the theory allow for the Minkowski vacuum. In this limit (though without consideration of the strongly coupled scalar field) post-Newtonian coefficients of spherically symmetric solutions coincide with those of the General Relativity. Thus the deviations from the convenient GR should be tested beyond the post-Newtonian corrections, that is for a system with strong gravity at astrophysical scales. In this Letter we consider potentially observable properties of black holes in the deformed Horava–Lifshitz gravity with Minkowski vacuum: the gravitational lensing and quasinormal modes. We have showed that the bending angle is seemingly smaller in the considered Horava–Lifshitz gravity than in GR. The quasinormal modes of black holes are longer lived and have larger real oscillation frequency in the Horava–Lifshitz gravity than in GR. These corrections should be observable in the near future experiments on lensing and by gravitational antennas, helping to constrain parameters of the Horava–Lifshitz gravity or to discard it. 相似文献
14.
We look for a Brans-Dicke type generalization of Horava-Lifshitz gravity. It is shown that such a generalization is possible within the detailed balance condition. Classically, the resulting theory reduces in the low energy limit to the usual Brans-Dicke theory with a negative cosmological constant for certain values of parameters. We then consider homogeneous, isotropic cosmology and study the effects of the new terms appearing in the model. 相似文献
15.
A. Dutta J.K. Bhattacharjee B.K. Chakrabarti 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,3(1):97-103
We have discussed the zero-temperature quantum phase transition in n-component quantum rotor Hamiltonian in the presence of regular frustration in the interaction. The phase diagram consists
of ferromagnetic, helical and quantum paramagnetic phase, where the ferro-para and the helical-para phase boundary meets at
a multicritical point called a (d,m) quantum Lifshitz point where (d,m) indicates that the m of the d spatial dimensions incorporate frustration. We have studied the Hamiltonian in the vicinity of the quantum Lifshitz point
in the spherical limit and also studied the renormalisation group flow behaviour using standard momentum space renormalisation
technique (for finite n). In the spherical limit ()one finds that the helical phase does not exist in the presence of any nonvanishing quantum fluctuation for m =d though the quantum Lifshitz point exists for all d > 1+m/2, and the upper critical dimensionality is given by d
u
= 3 +m/2. The scaling behaviour in the neighbourhood of a quantum Lifshitz point in d dimensions is consistent with the behaviour near the classical Lifshitz point in (d+z) dimensions. The dynamical exponent of the quantum Hamiltonian z is unity in the case of anisotropic Lifshitz point (d>m) whereas z=2 in the case of isotropic Lifshitz point (d=m). We have evaluated all the exponents using the renormalisation flow equations along-with the scaling relations near the
quantum Lifshitz point. We have also obtained the exponents in the spherical limit (). It has also been shown that the exponents in the spherical model are all related to those of the corresponding Gaussian
model by Fisher renormalisation.
Received: 23 December 1997 / Received in final form: 6 January 1998 / Accepted: 7 January 1998 相似文献
16.
We generalize Penrose’s notion of conformal infinity of spacetime, to situations with anisotropic scaling. This is relevant not only for Lifshitz-type anisotropic gravity models, but also in standard general relativity and string theory, for spacetimes exhibiting a natural asymptotic anisotropy. Examples include the Lifshitz and Schrödinger spaces (proposed as AdS/CFT duals of nonrelativistic field theories), warped AdS 3, and the near-horizon extreme Kerr geometry. The anisotropic conformal boundary appears crucial for resolving puzzles of holographic renormalization in such spacetimes. 相似文献
17.
ABBAS G. 《中国科学:物理学 力学 天文学(英文版)》2014,57(4):604-607
In this Letter,we examine the phantom energy accretion onto a Kehagias-Sfetsos black hole in Horava-Lifshitz gravity.To discuss the accretion process onto the black hole,the equations of phantom flow near the black hole have been derived.It is found that mass of the black hole decreases because of phantom accretion.We discuss the conditions for critical accretion.Graphically,it has been found that the critical accretion phenomena is possible for different values of parameters.The results for the Schwarzschild black hole can be recovered in the limiting case. 相似文献
18.
With R2 and R3 corrections to asymptotical Lifshitz space-time,we obtain pure Lovelock gravity solution and solution with non-trivial matter in 7-dimensional space-time. Then we obtain the general solution for any arbitrary dimensional space. In this paper, we also study black brane solutions in 7-dimensional Lifshitz space-time via the method of perturbation. And we popularize the black brane solution to arbitrary higher dimensions and discuss the
ratio of shear viscosity to entropy density ratioη/s. Then we analyze the result ofη/s to find that the correction of n-th (n≥3) order Lovelock term has trivial influence toη/s. 相似文献
19.
We study the one-loop effective potentials of the four-dimensional Lifshitz scalar field theory with the particular anisotropic scaling z=2, and the mass and the coupling constants renormalization are performed whereas the finite counterterm is just needed for the highest order of the coupling because of the mild UV divergence. Finally, we investigate whether the critical temperature for the symmetry breaking can exist or not in this approximation. 相似文献
20.
J. Klusoň S. Nojiri S. D. Odintsov D. Sáez-Gómez 《The European Physical Journal C - Particles and Fields》2011,71(7):1690
This paper is devoted to the study of various aspects of projectable F(R) Hořava–Lifshitz (HL) gravity. We show that some versions of F(R) HL gravity may have stable de Sitter solution and unstable flat-space solution. In this case, the problem of scalar graviton
does not appear because flat space is not vacuum state. Generalizing the U(1) HL theory proposed in , we formulate U(1) extension of scalar theory and of F(R) Hořava–Lifshitz gravity. The Hamiltonian approach for such the theory is developed in full detail. It is demonstrated that
its Hamiltonian structure is the same as for the non-relativistic covariant HL gravity. The spectrum analysis performed around
the flat background indicates the consistency of the theory because it contains a graviton with only transverse polarization.
Finally, we analyze the spatially flat FRW equations for U(1) invariant F(R) Hořava–Lifshitz gravity. 相似文献