The model of low-energy quantum gravity by the author has the property of asymptotic freedom at very short distances. The character of transition to asymptotic freedom is studied here. It is shown that this transition is not universal, but the one obeys the scaling rule: the range of this transition in units of $r/E^{1/2}$, where $r$ is a distance between particles and $E$ is an energy of the screening particle, is the same for any micro-particle. This range for a proton is between $10^{-11} - 10^{-13}$ meter, while for an electron it is approximately between $10^{-13} - 10^{-15}$ meter.
It is suggested in the model of low-energy quantum gravity by the author, that the background of super-strong interacting gravitons exists. It is shown here that micro-particles at very small distances should be almost free if the gravitational attraction is caused by a pressure of these gravitons.
We show that the recent claim that the 2+1 dimensional Ashtekar formulation for General Relativity has a finite number of physical degrees of freedom is not correct.
We investigate the Hamiltonian formulation of $f(T)$ gravity and find that there are five degrees of freedom. The six first class constraints corresponding to the local Lorentz transformation in Teleparallel gravity become second class constraints in $f(T)$ gravity, which leads to the appearance of three extra degrees of freedom and the violation of the local Lorentz invariance in $f(T)$ gravity. In general, there are $D-1$ extra degrees of freedom for $f(T)$ gravity in $D$ dimensions, and this implies that the extra degrees of freedom correspond to one massive vector field or one massless vec…
We study the behaviour of Yang-Mills theory under the inclusion of gravity. In the weak- gravity limit, the running gauge coupling receives no contribution from the gravitational sector, if all symmetries are preserved. This holds true with and without cosmological constant. We also show that asymptotic freedom persists in general field-theory-based gravity scenarios including gravitational shielding as well as asymptotically safe gravity.
Within the general framework of spatially covariant theories of gravity, we study the conditions for having only the two tensorial degrees of freedom. Generally, there are three degrees of freedom propagating in the theory, of which two are tensorial and one is of the scalar type. Through a detailed Hamiltonian analysis, we find two necessary and sufficient conditions to evade the scalar type degree of freedom. The first condition implies that the lapse-extrinsic curvature sector must be degenerate. The second condition ensures that the dimension of the phase space at each spacetime point is e…
f(T) gravity is a generalization of the teleparallel equivalent of general relativity (TEGR), where T is the torsion scalar made up of the Weitzenböck connection. This connection describes a spacetime with zero curvature but with nonvanishing torsion, which fully encodes the gravitational phenomena. We will present recent results in f(T) gravity related with the issue of the degrees of freedom of the theory. In particular, we discuss the recent finding that f(T) gravity has one extra degree of freedom compared with TEGR, which was concluded through a detailed Hamiltonian analysis of the constr…
Spherically symmetric space-times provide many examples for interesting black hole solutions, which classically are all singular. Following a general program, space-like singularities in spherically symmetric quantum geometry, as well as other inhomogeneous models, are shown to be absent. Moreover, one sees how the classical reduction from infinitely many kinematical degrees of freedom to only one physical one, the mass, can arise, where aspects of quantum cosmology such as the problem of initial conditions play a role.
The relation between an isotropic and an anisotropic model in loop quantum cosmology is discussed in detail, comparing the strict symmetry reduction with a perturbative implementation of symmetry. While the latter cannot be done in a canonical manner, it allows to consider the dynamics including the role of small non-symmetric degrees of freedom for the symmetric evolution. This serves as a model for the general situation of perturbative degrees of freedom in a background independent quantization such as loop quantum gravity, and for the more complicated addition of perturbative inhomogeneitie…
We have computed the number of polarization modes of gravitational waves propagating in the Minkowski background in $f(R)$ gravity. This is three of two from transverse-traceless tensor modes and one from a massive trace mode, which confirms the results found in the literature. There is no massless breathing mode and the massive trace mode corresponds to the Ricci scalar. A newly defined metric tensor in $f(R)$ gravity satisfies the transverse-traceless (TT) condition as well as the TT wave equation.
The degrees of freedom of multiway junctions in three dimensional gravity
Universidad Andres Bello（安德烈斯贝洛大学）；University of the Witwatersrand（威特沃特斯兰德大学）；Pontificia Universidad Católica de Valparaíso（天主教瓦尔帕莱索大学）；Universidad Técnica Federico Santa María（费德里科·圣玛丽亚技术大学）
We comment on some peculiarities of matter with and without Weyl invariance coupled to classical $2d$ Einstein-Hilbert gravity for several models, in particular, related to the counting of degrees of freedom and on the dynamics. We find that theories where the matter action is Weyl invariant has generically more degrees of freedom than action without the invariance. This follows from the Weyl invariance of the metric equations of motion independently of the invariance of the action. Then, we study another set of models with scalar fields and show that solutions to the equations of motion are e…
A canonical analysis for general relativity is performed on a null surface without fixing the diffeomorphism gauge, and the canonical pairs of configuration and momentum variables are derived. Next to the well-known spin-2 pair, also spin-1 and spin-0 pairs are identified. The boundary action for a null boundary segment of spacetime is obtained, including terms on codimension two corners.
We study in a systematic way a generic nonderivative (massive) deformation of general relativity using the Hamiltonian formalism. The number of propagating degrees of freedom is analyzed in a nonperturbative and background independent way. We show that the condition of having only five propagating degrees of freedom can be cast in a set of differential equations for the deforming potential. Though the conditions are rather restrictive, many solutions can be found.
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 consider massive higher-spin multiplets coupled to quantum gravity and compute their contributions to the gravitational beta functions at one loop. Such theories, if quantized with the Feynman prescription, would contain ghosts. Instead, those degrees of freedom are turned into purely virtual particles by means of the fakeon prescription and the resulting theories are both renormalizable and unitary. We extract the necessary number of fields to obtain asymptotic freedom by solving the relevant renormalization-group equations in the ultraviolet limit. We show that in the case of irreducible …
We identify different helicity degrees of freedom of Fierz-Paulian massive gravity around generic backgrounds. We show that the two-parameter family proposed by de Rham, Gabadadze, and Tolley always propagates five degrees of freedom and therefore is free from the Boulware-Deser ghost. The analysis has a number of byproducts, among which (a) it shows how the original decoupling limit construction ensures ghost freedom of the full theory, (b) it reveals an enhanced symmetry of the theory around linearized backgrounds, and (c) it allows us to give an algorithm for finding dispersion relations. T…
In the literature on $f(T)$ gravity, the status of local Lorentz invariance and the number of physical degrees of freedom have been controversial issues. Relying on a detailed Hamiltonian analysis, we show that there are several scenarios describing how local Lorentz invariance can be broken, but in the generic case, the number of physical degrees of freedom is found to be $N^*=5$; in $D$ dimensions, this number is $N^*=D(D-3)/2+(D-1)$. As expected, the theory is vulnerable to having problematical propagating modes. We compare our results with those existing in the literature. As a byproduct o…
Fourth order derivative gravity in 3+1-dimensions is perturbatively renormalizable and is shown to describe a unitary theory of gravitons in a limited coupling parameter space. The running gravitational constant which includes graviton contribution is computed. Generically, gravitational Newton's constant vanishes at short distances in this perturbatively renormalizable and unitary theory.
Removing spurious degrees of freedom from EFT of gravity
Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；The University of Tokyo（东京大学）
We investigate the linear cosmological perturbations of Hořava-Lifshitz gravity in a FRW universe without any matter. Our results show that a new gauge invariant dynamical scalar mode emerges, due to the gauge transformation under the "foliation-preserving" diffeomorphism and "projectability condition", and it can produce a scale invariant power spectrum. In the infrared regime with $λ=1$, the dynamical scalar degree of freedom turns to be a non-dynamical one at the linear order level.
Einstein-Strauss Hermitian gravity was recently formulated as a gauge theory where the tangent group is taken to be the pseudo-unitary group instead of the orthogonal group. A Higgs mechanism for massive gravity was also formulated. We generalize this construction to obtain massive Hermitian gravity with the use of a complex Higgs multiplet. We show that both the graviton and antisymmetric tensor acquire the same mass. At the linearized level, the theory is ghost free around Minkowski background and describes a massive graviton with five degrees of freedom and an antisymmetric field with three…
I show that the principle of equipartition, applied to area elements of a surface which are in equilibrium at the local Davies-Unruh temperature, allows one to determine the surface number density of the microscopic spacetime degrees of freedom in any diffeomorphism invariant theory of gravity. The entropy associated with these degrees of freedom matches with the Wald entropy for the theory. This result also allows one to attribute an entropy density to the spacetime in a natural manner. The field equations of the theory can then be obtained by extremising this entropy. Moreover, when the micr…
Nonlocal terms in the Einstein Hilbert(EH) action appears as IR corrections in effective theory of quantum gravity. Here we have considered such an action keeping the terms which are quadratic in Ricci Scalar. We obtain the solution for a spherical symmetric. We conduct an analysis for linearised gravity action and find the Newtonian potentials of linearized gravity action and count the degrees of freedom. Finally we reproduce the results for few known examples found in literature.
Typically higher-derivative theories are unstable. Instabilities manifest themselves from extra propagating degrees of freedom, which are unphysical. In this paper, we will investigate an infinite derivative field theory and study its true dynamical degrees of freedom via Hamiltonian analysis. In particular, we will show that if the infinite derivatives can be captured by a Gaussian kinetic term, i.e. exponential of entire function, then it is possible to prove that there are only finite number of dynamical degrees of freedom. We will further extend our investigation into infinite derivative t…
Two models of dilatonic gravity are investigated: (i) dilaton-Yang-Mills gravity and (ii) higher-derivative dilatonic gravity. Both are renormalizable in $2+ε$ dimensions and have a smooth limit for $ε\rightarrow 0$. The corresponding one-loop effective actions and beta-functions are found. Both theories are shown to possess a non-trivial ultraviolet fixed point ---for all dilatonic couplings--- in which the gravitational constant is asymptotically free. It is shown that in the regime of asymptotic freedom the matter central charge can be significantly increased by two different mechanisms ---…
We assume that the fourdimensional quantum gravity is scale invariant at short distances. We show through a simple scaling argument that correlation functions of quantum fields interacting with gravity have a universal (more regular) short distance behavior.
It is possible to provide a physical interpretation for the field equations of gravity based on a thermodynamical perspective. The virtual degrees of freedom associated with the horizons perceived by the local Rindler observers, play a crucial role in this approach. In this context, the relation S=E/2T between the entropy (S), active gravitational mass (E) and temperature (T) - obtained previously in gr-qc/0308070 [CQG, 21, 4485 (2004)] - can be reinterpreted as the law of equipartition E = (1/2) nkT where n=A/L_P^2 is the number (density) of microscopic horizon degrees of freedom. Conversely,…
A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity. The underlying constraints present a consistent deformation of the classical system, which shows that the discreteness in loop quantum gravity can be implemented in effective equations without spoiling space-time covariance. Nevertheless, non-trivial quantum corrections do arise in the constraint algebra. Since correction terms must appear in tightly controlled forms to avoid anomalies, detailed in…
In this note, we attempt to provide some insights into the structure of non-perturbative descriptions of quantum gravity using known examples of gauge-theory / gravity duality. We argue that in familiar examples, a quantum description of spacetime can be associated with a manifold-like structure in which particular patches of spacetime are associated with states or density matrices in specific quantum systems. We argue that quantum entanglement between microscopic degrees of freedom plays an essential role in the emergence of a dual spacetime from the nonperturbative degrees of freedom. In par…
Runaway solutions can be avoided in fourth order gravity by a doubling of the matter operator algebra with a symmetry constraint with respect to the exchange of observable and hidden degrees of freedom together with the change in sign of the ghost and the dilaton fields. The theory is classically equivalent to Einstein gravity, while its non-unitary Newtonian limit is shown to lead to a sharp transition, around $10^{11}$ proton masses, from the wavelike properties of microscopic particles to the classical behavior of macroscopic bodies, as well as to a trans-Planckian regularization of collaps…
We undertake a complete and covariant treatment for the quadratic Lagrangian of all of the degrees of freedom of massive gravity with a fixed flat fiducial metric for arbitrary massive gravity parameters around any isotropic self-accelerating background solution. Generically, 3 out of 4 Stuckelberg degrees of freedom propagate in addition to the usual 2 tensor degrees of freedom of general relativity. The complete kinetic structure typically is only revealed at an order in the graviton mass that is equivalently to retaining curvature terms in a locally flat expansion. These results resolve sev…
We study almost universal spacetimes - spacetimes for which the field equations of any generalized gravity with the Lagrangian constructed from the metric, the Riemann tensor and its covariant derivatives of arbitrary order reduce to one single differential equation and one algebraic condition for the Ricci scalar. We prove that all d-dimensional Kundt spacetimes of Weyl type III and traceless Ricci type N are almost universal. Explicit examples of Weyl type II almost universal Kundt metrics are also given. The considerable simplification of the field equations of higher-order gravity theories…
Considering the quantum statistics of the degrees of freedom on the holographic screen it is shown that the ratio of the number of excited bulk degrees of freedom to the number of excited surface degrees of freedom, is given by the MOND interpolating function μ. This relationship is shown to hold also in AQUAL, and in the extension of MOND to de Sitter space. Based on the relationship between the entropy, and the number of degrees of freedom on the holographic screen, a simple expression, relating the MOND interpolating function to the ratio of the two-dimensional entropy to Bekenstein-Hawking…
I wish to expound a novel perspective of probing universal character of gravity. To begin with, inclusion of zero mass particle in mechanics leads to special relativity while its interaction with a universal force shared by all particles leads to general relativity. The universal nature of force further suggests that it is intrinsically attractive, self interactive and higher dimensional. I argue that the principle of universality could serve as a good guide for future directions.
We study a modification of the Plebanski action for general relativity, which leads to a modified theory of gravity with eight degrees of freedom. We show how the action can be recasted as a bi-metric theory of gravity, and expanding around a bi-flat background we identify the six extra degrees of freedom with a second, massive graviton and a scalar mode.
In this paper, we investigate a scenario in which late time cosmic acceleration might arise due to coupling between dark matter and baryonic matter without resorting to dark energy or large scale modification of gravity associated with extra degrees of freedom. The scenario can give rise to late time acceleration in Jordan frame and no acceleration in Einstein frame - \textit{generic modification of gravity} caused by disformal coupling. Using a simple parametrization of the coupling function, in maximally disformal case, we constrain the model parameters by using the age constraints due to gl…
The study of linear perturbation theory for general functions of the Ricci and Gauss-Bonnet scalars is done over an empty anisotropic universe, i.e. the Kasner-type background, in order to show that an anisotropic background in general has ghost degrees of freedom, which are absent on Friedmann-Lemaitre-Robertson-Walker (FLRW) backgrounds. The study of the scalar perturbation reveals that on this background the number of independent propagating degrees of freedom is four and reduces to three on FLRW backgrounds, as one mode becomes highly massive to decouple from the physical spectrum. When th…
Models of loop quantum gravity based on real connections have a deformed notion of general covariance, which leads to the phenomenon of signature change. This result is confirmed here in a general analysis of all midisuperspace models without local degrees of freedom. As a subclass of models, 2-dimensional theories of dilaton gravity appear, but a larger set of examples is possible based only on the condition of anomaly freedom. While the classical dilaton gravity models are the only such systems without deformed covariance, they do give rise to signature change when holonomy modifications are…
On the basis of the idea that gravity defines a universal UV-completion and using a form of UV/IR correspondence we revisit some Swampland conjectures, in particular de Sitter and infinite distance conjectures, from the point of view of renormalization group energy flow. The rol and limitations of non perturbative instanton effects to define a metastable cosmological constant are briefly discussed in this context.
On the basis of a limited number of reasonable axioms, we discuss the classification of all the possible universality classes of diffeomorphisms invariant metric theories of quantum gravity. We use the language of the renormalization group and adopt several ideas which originate in the context of statistical mechanics and quantum field theory. Our discussion leads to several ideas that could affect the status of the asymptotic safety conjecture of quantum gravity and give universal arguments towards its proof.
In a recent paper we have analyzed the role that a universal set of local symmetries plays in suppressing the superposition principle in classical mechanics via a path-integral formulation of classical mechanics itself. In this paper first we generalize those symmetries, second we study the role which the gauge fixing plays and third we put forward the idea of which ones should be the physical degrees of freedom of the theory.
Spatially covariant gravity with two degrees of freedom: A perturbative analysis up to cubic order
Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University（天津大学理学院物理系联合量子研究中心）；School of Physics and Astronomy, Sun Yat-sen University（中山大学物理与天文学院）；Institute for Gravitational Wave Astronomy, Henan Academy of Sciences（河南省科学院引力波天文研究所）；School of Physics, Sun Yat-sen University（中山大学物理学院）；Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing, Sun Yat-sen University（中山大学广东省量子计量与传感重点实验室）
We study the renormalization group flow of higher derivative gravity, utilizing the functional renormalization group equation for the average action. Employing a recently proposed algorithm, termed the universal renormalization group machine, for solving the flow equation, all the universal features of the one-loop beta-functions are recovered. While the universal part of the beta-functions admits two fixed points, we explicitly show that the existence of one of them depends on the choice of regularization scheme, indicating that it is most probably unphysical.
Based on the ultraviolet asymptotic freedom of nonlocal quantum gravity, we show that the trans-Planckian energy regime is unattainable in laboratory experiments. As physical implications, it turns out that the violation of causality, typical of nonlocal field theories, can never be detected in particle accelerators, while the asymptotic freedom of the theory provides an elegant solution to the so called trans-Planckian cosmological problem.
We compute non-perturbative flow equations for the couplings of quantum gravity in fourth order of a derivative expansion. The gauge invariant functional flow equation for arbitrary metrics allows us to extract $β$-functions for all couplings. In our truncation we find two fixed points. One corresponds to asymptotically free higher derivative gravity, the other is an extension of the asymptotically safe fixed point in the Einstein-Hilbert truncation or extensions thereof. The infrared limit of the flow equations entails only unobservably small modifications of Einstein gravity coupled to a sca…
The universal thermodynamic relations between corrections to entropy and extremality for various black holes solutions have been studied. In this regard, we hereby consider a number of different black brane solutions in different structures for perturbative corrections to general relativity. These are, namely, black brane solution in Rastall AdS massive gravity, Einstein-Yang-Mills AdS black brane solution in massive gravity and general anisotropic black brane in Horava-Lifshitz gravity. We calculate both the entropy and extremality bound by introducing a small constant correction to the actio…
We investigate the asymptotic safety scenario for a scalar-gravity system. This system contains two avatars of the dynamical Newton coupling, a gravitational self-coupling and a scalar-graviton coupling. We uncover an effective universality for the dynamical Newton coupling on the quantum level: its momentum-dependent avatars are in remarkable quantitative agreement in the scaling regime of the UV fixed point. For the background Newton coupling, this effective universality is not present, but qualitative agreement remains.
We search for a universal property of quantum gravity. By "universal", we mean the independence from any existing model of quantum gravity (such as the super string theory, loop quantum gravity, causal dynamical triangulation, and so on). To do so, we try to put the basis of our discussion on theories established by some experiments. Thus, we focus our attention on thermodynamical and statistical-mechanical basis of the black hole thermodynamics: Let us assume that the Bekenstein-Hawking entropy is given by the Boltzmann formula applied to the underlying theory of quantum gravity. Under this a…
We prove the equivalence between non-local gravity with an arbitrary form factor and a non-local gravitational system with an extra rank-2 symmetric tensor. Thanks to this reformulation, we use the diffusion-equation method to transform the dynamics of renormalizable non-local gravity with exponential operators into a higher-dimensional system local in spacetime coordinates. This method, first illustrated with a scalar field theory and then applied to gravity, allows one to solve the Cauchy problem and count the number of initial conditions and of non-perturbative degrees of freedom, which is …
Graviton propagation in ghost-free massive gravity
Abdus Salam Centre for Theoretical Physics, Imperial College（帝国理工学院阿卜杜斯·萨拉姆理论物理中心）；Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICC), Universitat de Barcelona（巴塞罗那大学量子天体物理学系及宇宙科学研究所）
