Michael A. Ivanov
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.
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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.
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…
On the Degrees of Freedom of $R^2$ Gravity in Flat Spacetime
本文用Stueckelberg重写和直接考察度规微扰两种方法研究平直时空中$R^2$引力的自由度，发现纯理论无自由度，并证明完整与纯理论的表观不连续性仅为微扰假象。
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
本文证明三维引力中的n路结对应于n-1条耦合弦，每条弦在光滑化背景中满足Nambu-Goto方程，并带有类似Monge-Ampère的耦合项，且这些自由度在零张力极限下存活，表明纯引力可产生类物质行为。
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
本文针对含黎曼张量三次项的广义相对论，采用作用量法去除虚假自由度，得到仅传播无质量自旋2引力子的最小修正引力，表明该类理论可作为捕获未知紫外效应的引力有效理论。
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.
Asymptotic freedom in (3+1)-dimensional projectable Horava gravity: connecting ultraviolet to infrared
该研究探究(3+1)维可投影霍拉瓦引力的重整化群流，发现其存在渐近自由不动点及连接紫外不动点与红外广义相对论形式区域的轨迹，揭示引力耦合在紫外和红外区均消失的非单调行为。
Running of the Number of Degrees of Freedom in Quantum Conformal Gravity
研究Weyl共形引力中自由度随能量尺度的运行，通过Fradkin--Tseytlin方案和基于$a$-、$c$-函数的计数方法，证明自由度从UV区域的六个开始单调递减且与背景无关。
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 ---…
Boundary freedom in higher spin gravity
本文研究了三维渐近反德西特高自旋引力中允许任意边界自由度的新边界条件，发现了扩大的渐近荷代数和对偶场论新反常，并将这些反常效应扩展至渐近平坦时空。
A Non-linear Massive Gravity Theory of Geometric Origin
该研究分析挠率引力理论中非线性阶的传播自由度，发现挠率双引力子族中挠率场的自由度从线性阶的五个变为非线性阶的九个。
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…
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…
Nonlinear Degrees of Freedom of Born-Infeld New Massive Gravity
本文通过非线性正则分析证明Born-Infeld新引力理论在正则分支上仅有两个局部自由度，不传播额外的Boulware-Deser型标量模式。
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…
Dirac-Bergmann analysis and Degrees of Freedom of Coincident $f(Q)$-gravity
本文通过Dirac-Bergmann分析研究了重合f(Q)引力在4维时空中的传播自由度，发现该理论一般具有6个传播自由度且无剩余规范自由度，并探讨了出现7个自由度的条件。
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 occasion of the 25th anniversary of Asymptotic Freedom, celebrated at the QCD Euroconference 98 on Quantum Chromodynamics, Montpellier, July 1998, I described the discovery of Asymptotic Freedom and the emergence of QCD.
Spatially covariant gravity with two degrees of freedom: A perturbative analysis up to cubic order
本文通过扰动方法分析了具有两个自由度的时空协变引力理论，在立方阶内推导出五个满足条件的拉格朗日量。
Discreteness Unravels the Black Hole Information Puzzle: Insights from a Quantum Gravity Toy Model
本文提出黑洞Planck尺度微观自由度能提纯信息且不显著贡献能量，从而解决信息难题，并通过受圈量子引力启发的可解玩具模型验证了该机制。
Recently, a rank four tensor group field theory has been proved renormalizable. We provide here the key points on the renormalizability of this model and its UV asymptotic freedom.
Counting Degrees of Freedom: A Method Applicable from Scalars to f(Q) Gravity and Beyond
本文提出一种直接作用于场方程、非拉格朗日也非哈密顿的逐步方法，用于计算一般场论自由度并识别约束，并成功应用于传统 Dirac-Bergmann 算法失效的 f(Q) 引力，得到七个传播自由度。
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…
We utilize Coleman's theorem and show that quantum chromodynamics based on asymptotic freedom and confinement must have chiral symmetry realized as a spontaneously broken symmetry.
This is an introduction to asymptotically safe quantum gravity, explaining the main idea of asymptotic safety and how it could solve the problem of predictivity in quantum gravity. In the first part, the concept of an asymptotically safe fixed point is discussed within the functional Renormalization Group framework for gravity, which is also briefly reviewed. A concise overview of key results on asymptotically safe gravity is followed by a short discussion of important open questions. The second part highlights how the interplay with matter provides observational consistency tests for all quan…
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
研究无鬼大规模引力中两种可能的质量项，探讨引力子在不同背景下的传播特性，证明高频率极限下二阶引力子始终沿度规光锥传播。
The ultraviolet completion of gauge theories by higher derivative terms can dramatically change their behavior at high energies. The requirement of asymptotic freedom imposes very stringent constraints that are only satisfied by a small family of higher derivative theories. If the number of derivatives is large enough ($n > 4$) the theory is strongly interacting both at extreme infrared and ultraviolet regimes whereas it remains asymptotically free for a low number of extra derivatives ($n \leqslant 4$). In all cases the theory improves its ultraviolet behavior leading in some cases to ultravi…
We study the recently proposed Covariant Renormalizable Gravity (CRG), which aims to provide a generally covariant ultraviolet completion of general relativity. We obtain a space-time 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 h…
Freelance Holography, Part I: Setting Boundary Conditions Free in Gauge/Gravity Correspondence
本文利用协变相空间形式中的 W、Y、Z 自由度阐明规范/引力对应中边界条件与辛结构的对应关系，并据此提出可自由选择引力侧边界条件的自由全息术框架。
In general relativity, the fields on a black hole horizon are obtained from those in the bulk by pullback and restriction. Similarly, in quantum gravity, the quantized horizon degrees of freedom should result from restricting, or pulling-back, the quantized bulk degrees of freedom. This is not yet fully realized in the - otherwise very successful - quantization of isolated horizons in loop quantum gravity. In this work we outline a setting in which the quantum horizon degrees of freedom are simply components of the quantized bulk degrees of freedom. There is no need to quantize them separately…
We establish that there is no finite PT-symmetric Quantum Electrodynamics (QED) and as a consequence the Callan-Symanzik function $β(α)<0$ for all $α$ greater than zero: PT-symmetric QED exhibits both asymptotic freedom and infrared slavery.
Matter-quantum gravity interactions can be used for direct and also indirect experimental tests of quantum gravity. We focus on photon-photon scattering in asymptotically safe gravity as a direct test of the small-scale structure of spacetime, and discuss how near-future experiments can probe asymptotic safety in a setting with large extra dimensions.
We investigate the Hamiltonian structure of a class of gravitational theories whose actions are linear in the lapse function. We derive the necessary and sufficient condition for a theory in this class to have two or less local physical degrees of freedom. As an application we then find several concrete examples of modified gravity theories in which the total number of local physical degrees of freedom in the gravity sector is two.
Form factors constitute the key building block when organising the gravitational dynamics in terms of a curvature expansion. They generalise the concept of momentum-dependent couplings to curved spacetime. Moreover, they may capture modifications of the gravitational interactions at high energy scales in a non-perturbative way. We briefly review the role of form factors in various quantum gravity programmes with special emphasis on non-local, ghost-free gravity and asymptotically safe gravity. In this context, we introduce a quantum gravity motivated scalar toy model, which demonstrates that L…
We investigate the non-perturbative degrees of freedom of a class of weakly non-local gravitational theories that have been proposed as an ultraviolet completion of general relativity. At the perturbative level, it is known that the degrees of freedom of non-local gravity are the same of the Einstein--Hilbert theory around any maximally symmetric spacetime. We prove that, at the non-perturbative level, the degrees of freedom are actually eight in four dimensions, contrary to what one might guess on the basis of the "infinite number of derivatives" present in the action. It is shown that six of…
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