We will construct a loop space formalism for general relativity, and construct the Polyakov variables as connections for such a loop space. We will use these Polyakov variables to construct a dual theory of gravity beyond linear approximation. It will be demonstrated that this loop space duality reduces to the Hodge duality for linearized gravity. Furthermore, a loop space curvature will be constructed from this Polyakov variable. It will be shown that this loop space curvature vanishes in the absence of topological defects, and so it can be used to investigate gravitational monopoles. We will also construct the suitable monopole charge for such gravitational monopoles.
Four--dimensional Einstein--Maxwell--dilaton--axion system restricted to space--times with one non--null Killing symmetry is formulated as the three--dimensional gravity coupled sigma--model. Several alternative representations are discussed and the associated hidden symmetries are revealed. The action of target space isometries on the initial set of (non--dualized ) variables is found. New mulicenter solutions are obtained via generating technique based on the formulation in terms of the non--dualized variables.
In two space-time dimensions, there is a theory of Lorentzian quantum gravity which can be defined by a rigorous, non-perturbative path integral and is inequivalent to the well-known theory of (Euclidean) quantum Liouville gravity. It has a number of appealing features: i) its quantum geometry is non-fractal, ii) it remains consistent when coupled to matter, even beyond the c=1 barrier, iii) it is closer to canonical quantization approaches than previous path-integral formulations, and iv) its construction generalizes to higher dimensions.
An interesting proposal has recently been made to extend massive gravity models beyond dRGT by a disformal transformation of the metric. In this Letter we want to note that it can be viewed as a mimetic extension of dRGT gravity which enormously simplifies the Hamiltonian analysis. In particular, pure gravity sector is equivalent to the usual dRGT gravity coupled to a constrained scalar field. And we also give some comments about possible matter couplings.
Some conceptual issues concerning $f(T)$ theories --a family of modified gravity theories based on absolute parallelism-- are analyzed. Due to the lack of local Lorentz invariance, the autoparallel frames satisfying the field equations are evasive to an \emph{a priori} physical understanding. We exemplify this point by working out the vierbein (tetrad) fields for closed and open Friedmann-Robertson-Walker cosmologies.
Black hole event horizons and cosmological event horizons share many properties, making it natural to ask whether our recent advances in understanding black holes generalize to cosmology. To this end, we discuss a paradox that occurs if observers can access what lies beyond their cosmological horizon in the same way that they can access what lies beyond a black hole horizon. In particular, distinct observers with distinct horizons may encode the same portion of spacetime, violating the no-cloning theorem of quantum mechanics. This paradox is due precisely to the observer-dependence of the cosm…
A supergravity extension of the $(R+R^2)$ gravity with the additional (Born-Infeld) structure of a massive vector multiplet gives rise to the specific $F(R)$ gravity, whose structure is investigated in detail. The massive vector multiplet has inflaton (scalaron), goldstino and a massive vector field as its field components. The model describes Starobinsky inflation and allows us to extrapolate the $F(R)$ function beyond the inflationary scale (up to Planck scale). We observe some differences versus the $(R+R^2)$ gravity, and several breaking patterns of the well known correspondence between th…
We study the Faddeev-Popov ghost sector of asymptotically safe quantum gravity, which becomes non-perturbative in the ultraviolet. We point out that nonzero matter-ghost couplings and higher-order ghost self-interactions exist at a non-Gaussian fixed point for the gravitational couplings, i.e., in the ultraviolet. Thus the ghost sector in this non-perturbative ultraviolet completion does not keep the structure of a simple Faddeev-Popov determinant. We discuss implications of the new ghost couplings for the Renormalization Group flow in gravity, the form of the ultraviolet completion, and the r…
Scalar Gauss-Bonnet gravity is the only theory with quadratic curvature corrections to general relativity whose field equations are of second differential order. This theory allows for nonperturbative dynamical corrections and is therefore one of the most compelling case studies for beyond-general relativity effects in the strong-curvature regime. However, having second-order field equations is not a guarantee for a healthy time evolution in generic configurations. As a first step towards evolving black-hole binaries in this theory, we here derive the 3+1 decomposition of the field equations f…
Noncommutative geometry, in its many incarnations, appears at the crossroad of various researches in theoretical and mathematical physics: from models of quantum space-time (with or without breaking of Lorentz symmetry) to loop gravity and string theory, from early considerations on UV-divergencies in quantum field theory to recent models of gauge theories on noncommutative spacetime, from Connes description of the standard model of elementary particles to recent Pati-Salam like extensions. We list several of these applications, emphasizing also the original point of view brought by noncommuta…
We solve the Einstein equations in the Randall-Sundrum framework with a static, spherically symmetric matter distribution on the {\it physical brane} and obtain an approximate expression for the gravitational field outside the source to second order in the gravitational coupling. This expression when confined on the {\it physical brane} coincides with the standard form of the Schwarzschild metric. Therefore, the Randall-Sundrum scenario is consistent with the Mercury precession test of General Relativity.
It is commonly believed that the dRGT theory is the unique way to describe a massive spin-2 field without ghosts. While dRGT is arguably the most elegant massive gravity theory, it seems that it may not be the unique ghost-free one if one relaxes the assumption of locality. In this work, we derive a new massive gravity theory by using a disformal transformation of the metric tensor in the dRGT action. Its decoupling limit lives inside the class of beyond-Horndeski Lagrangians as long as the transformation of the metric remains purely disformal. This proves the absence of ghosts in this decoupl…
We outline a holographic recipe to reconstruct $α'$ corrections to AdS (quantum) gravity from an underlying CFT in the strictly planar limit ($N\rightarrow\infty$). Assuming that the boundary CFT can be solved in principle to all orders of the 't Hooft coupling $λ$, for scalar primary operators, the $λ^{-1}$ expansion of the conformal dimensions can be mapped to higher curvature corrections of the dual bulk scalar field action. Furthermore, for the metric pertubations in the bulk, the AdS/CFT operator-field isomorphism forces these corrections to be of the Lovelock type. We demonstrate this by…
Quantization of relativistic point particles coupled to three-dimensional Einstein gravity naturally leads to field theories living on the Lorentz group in their momentum representation. The Lie group structure of momentum space can be traced back to the classical phase space of the particles coupled to topological gravity. In this work we show how the non-trivial structure of momentum space leads to an unusual description of Fock space. The latter is reflected in a deformed algebra of creation and annihilation operators which reduces to the ordinary algebra when momentum space "flattens" to M…
We present qualitative arguments in favor of an extension of the theory of the gravitational interaction beyond that resulting from the Hilbert-Einstein action. To this end we consider a locally conformal invariant theory of gravity, discussed some thirty years ago by Mannheim and Kazanas. We discuss its exact solution of the static, spherically symmetric configurations and, based on these, we revisit some of the outstanding problems associated with gravity, high energy interactions and sketch potential resolutions within the conformal gravity framework.
In this text we outline the motivation for developping a quantum $S$-matrix approach for the classical gravitational two-body scattering. As an application we briefly present the derivation of black-hole metrics in various dimensions.
We propose a covariant entropy bound in gravitational theories beyond general relativity (GR), using Wald-Jacobson-Myers entropy instead of Bekenstein-Hawking entropy. We first extend the proof of the bound known in 4-dimensional GR to D-dimensional GR, f(R) gravity and canonical scalar-tensor theory. We then consider Einstein-Gauss-Bonnet (EGB) gravity as a more non-trivial example and, under a set of reasonable assumptions, prove the bound in the GR branch of spherically symmetric configurations. As a corollary, it is shown that under the null and dominant energy conditions, the generalized …
We study event horizon candidates for slowly evolving dynamical black holes in General Relativity and Einstein-Gauss-Bonnet (EGB) gravity. Such a type of horizon candidate has been termed as slowly evolving null surface (SENS). It signifies a near-equilibrium state of a dynamic black hole. We demonstrate the time evolution of such surfaces for three different metrics. First, we locate such a surface for a charged Vaidya metric and show that the parameter space of the black hole gets constrained to allow a physically admissible slowly evolving null surface. We then consider a supertranslated Va…
We obtain the conserved Abbott-Deser-Tekin (ADT)-{\it like} current for the Lanczos-Lovelock gravity for a diffeomorphism vector, which defines the horizon of a spacetime and, importantly, is not necessarily a Killing vector. As the original ADT current is defined only for the presence of a background Killing vector, one cannot use it extensively for the thermodynamic description of the wide classes of non-Killing horizons which appear in gravity. On the other hand, this general approach can be utilized for those horizons. Here, the conserved current can be written as the derivative of the two…
We solve the Wheeler-DeWitt equation for {\it four}-dimensional Einstein gravity as an expansion in powers of the Planck mass by means of a heat kernel regularization. Our results suggest that in the universe with a very small radius or with a very large curvature beyond a Planck scale expectation values of operators are reduced to calculations in a path integral representation of {\it three}-dimensional Einstein gravity.
We argue that the divergence in time for the asymptotic observer occurs because of specifying the position of the Horizon beyond the Planck scale. In fact, a similar divergence in time will also occur for an in-going observer in Gravity's Rainbow, if we again specify the position of the Horizon beyond the Planck scale. On the other hand, if we accept the occurrence of a minimum measurable length scale associated with a universal invariant maximum energy scale in Gravity's Rainbow, then the time taken by both the in-going and asymptotic observers will be finite.
We review the recent literature on modified theories of gravity in the Palatini approach. After discussing the motivations that lead to consider alternatives to Einstein's theory and to treat the metric and the connection as independent objects, we review several topics that have been recently studied within this framework. In particular, we provide an in-depth analysis of the cosmic speedup problem, laboratory and solar systems tests, the structure of stellar objects, the Cauchy problem, and bouncing cosmologies. We also discuss the importance of going beyond the f(R) models to capture other …
In this essay, I wish to share a novel perspective which envisions universalization as a guide from the classical world to relativistic and quantum world. It is the incorporation of zero mass particle in mechanics which leads to special relativity while its interaction with a universal field shared by all particles leads to general relativity. We also give a very simple classical argument to show that why the universal force has to be attractive. We try to envisage what sort of directions does this principle of universality point to for the world beyond general relativity?
The dS/CFT correspondence postulates the existence of a Euclidean CFT dual to a suitable gravity theory with Dirichlet boundary conditions asymptotic to de Sitter spacetime. A semi-classical model of such a correspondence consists of Einstein gravity with positive cosmological constant and without matter which is dual to Euclidean Liouville theory defined at the future conformal boundary. Here we show that Euclidean Liouville theory is also dual to Einstein gravity with Dirichlet boundary conditions on a fixed timelike slice in the static patch. Intriguingly, the spacetime interpretation of Eu…
The strong cosmic censorship conjecture (SCCC) proposed by Penrose states that the presence of the inner Cauchy horizon ($\mathcal{CH}$) in the black hole solutions does not threaten the deterministic nature of general relativity since it is actually unstable against the remnant perturbation fields that fall into the black hole. Although this conjecture is well-established for the asymptotically flat spacetimes in general relativity, it is challenged upon taking a small positive cosmological constant as required by observational data. This challenge can be fixed by finding even one type of qua…
We construct a plethora of new Euclidean AdS-Taub-NUT and bolt solutions of several four- and six-dimensional higher-curvature theories of gravity with various base spaces $\mathcal{B}$. In $D=4$, we consider Einsteinian cubic gravity, for which we construct solutions with $\mathcal{B}=\mathbb{S}^2,\mathbb{T}^2$. These represent the first generalizations of the Einstein gravity Taub-NUT/bolt solutions for any higher-curvature theory in four dimensions. In $D=6$, we show that no new solutions are allowed for any Generalized quasi-topological gravity at cubic order. They exist however when we co…
In the extended phase space approach, one can define thermodynamic pressure and volume that gives rise to the van der Waals type phase transition for black holes. For Einstein's GR, the expressions of these quantities are unanimously accepted. Of late, the van der Waals phase transition in black holes has been found in modified theories of gravity as well, such as the $f(R)$ gravity and the scalar-tensor gravity. However, in the case of these modified theories of gravity, the expression of pressure (and, hence, volume) is not uniquely determined. In addition, for these modified theories, the e…
We study the nature of constraints and the Hamiltonian structure in a scalar-tensor theory of gravity recently proposed by Gleyzes, Langlois, Piazza and Vernizzi (GLPV). For the simple case with A_5 = 0, namely when the canonical momenta conjugate to the spatial metric are linear in the extrinsic curvature, we prove that the number of physical degrees of freedom is three at fully nonlinear level, as claimed by GLPV. Therefore, while this theory extends Horndeski's scalar-tensor gravity theory, it is protected against additional degrees of freedom.
The back-reaction of a classical gravitational field interacting with quantum matter fields is described by the semiclassical Einstein equation, which has the expectation value of the quantum matter fields stress tensor as a source. The semiclassical theory may be obtained from the quantum field theory of gravity interacting with N matter fields in the large N limit. This theory breaks down when the fields quantum fluctuations are important. Stochastic gravity goes beyond the semiclassical limit and allows for a systematic and self-consistent description of the metric fluctuations induced by t…
A unified description of early-time inflation with the current cosmic acceleration is achieved by means of a new theory that uses a quadratic model of gravity, with the inclusion of an exponential $F(R)$-gravity contribution for dark energy. High-curvature corrections of the theory come from higher-derivative quantum gravity and yield an effective action that goes beyond the one-loop approximation. It is shown that, in this theory, viable inflation emerges in a natural way, leading to a spectral index and tensor-to-scalar ratio that are in perfect agreement with the most reliable Planck result…
We construct "soft-collinear gravity", the effective field theory which describes the interaction of collinear and soft gravitons with matter (and themselves), to all orders in the soft-collinear power expansion. Despite the absence of collinear divergences in gravity at leading power, the construction exhibits remarkable similarities with soft-collinear effective theory of QCD (gauge fields). It reveals an emergent soft background gauge symmetry, which allows for a manifestly gauge-invariant representation of the interactions in terms of a soft covariant derivative, the soft Riemann tensor, a…
We consider theories describing the dynamics of a four-dimensional metric, whose Lagrangian is diffeomorphism invariant and depends at most on second derivatives of the metric. Imposing degeneracy conditions we find a set of Lagrangians that, apart form the Einstein-Hilbert one, are either trivial or contain more than two degrees of freedom. Among the partially degenerate theories, we recover Chern-Simons gravity, endowed with constraints whose structure suggests the presence of instabilities. Then, we enlarge the class of parity violating theories of gravity by introducing new "chiral scalar-…
We argue in this essay that for classical configurations of gravity in the AdS/CFT setup, it is in general impossible to reconstruct the bulk geometry from the leading asymptotic behavior of the classical fields in gravity alone. This is possible sufficiently near the vacuum, but not more generally. We argue this by using a counter-example that utilizes the supersymmetric geometries constructed by Lin, Lunin, and Maldacena. In the dual quantum field theory, the additional data required to complete the geometry is encoded in modes that near the vacuum geometry lie beyond the Planck scale.
The Dirac theory of electron and QED neglect gravitational field, while the corresponding to electron Kerr-Newman gravitational field has very strong influence on the Compton distances. It polarizes space-time, deforms the Coulomb field and changes topology. We argue that the Kerr geometry may be hidden beyond the Quantum Theory, representing a complimentary space-time description.
Preface to Fields, Gravity, Strings and Beyond: In Memory of Stanley Deser
Université Libre de Bruxelles（布鲁塞尔自由大学）；International Solvay Institutes（国际索尔维研究所）；Collège de France, Université PSL（法兰西学院，巴黎文理研究大学）；Dipartimento di Fisica, Università di Firenze and INFN Sezione di Firenze（佛罗伦萨大学物理系和意大利国家核物理研究所佛罗伦萨分部）
There are many hints that gravity is asymptotically safe. The inclusion of gravitational corrections can result in the ultraviolet fundamental Standard Model and constrain the Higgs mass to take the smallest value such that electroweak vacuum is stable. Taking into account the current top quark mass measurements this value is $m_H \approx 130$ GeV.\\ This article considers the predictions of the Higgs mass in two minimal Beyond Standard Model scenarios, where the stability is improved. One is the sterile quark axion model, while the other is the $U(1)_{B-L}$ gauge symmetry model introducing a …
We show that the space of solutions of a wide family of Ricci-based metric-affine theories of gravity can be put into correspondence with the space of solutions of general relativity (GR). This allows us to use well-established methods and results from GR to explore new gravitational physics beyond it.
Perturbatively renormalizable higher-derivative gravity in four space-time dimensions with arbitrary signs of couplings has been considered. Systematic analysis of the action with arbitrary signs of couplings in lorentzian flat space-time for no-tachyons, fixes the signs. Feynman $+iε$ prescription for these sign further grants necessary convergence in path-integral, suppressing the field modes with large action. This also leads to a sensible wick rotation where quantum computation can be performed. Running couplings for these sign of parameters makes the massive tensor ghost innocuous leading…
We show that it is possible to go beyond the simple kinematical aspects of the analog models of gravity. We exhibit the form of the Lagrangian that describes the dynamics of a self-interacting field $ ϕ$ as an interaction between $ ϕ$ and its associated effective metric $ \hat{g}^{μν}.$ In other words the non-linear equation of motion of the field may be interpreted as the gravitational influence on $ ϕ$ by its own effective metric which, in our scheme becomes an active partner of the dynamics of $ ϕ. $
In the present paper, we briefly review recent studies of second-order gravitational perturbations in braneworld models. After we consider the possibility of pathological behavior of gravity at higher orders of perturbation, second-order perturbations are discussed in Randall-Sundrum braneworld models. Because the mass spectra in these braneworld models are different, we analyze them using different approaches. In the respective models, it is discussed that 4D Einstein gravity is approximately recovered at level of second-order perturbation, although there are some exceptional cases in the two…
The motion of test bodies in gravity is tightly linked to the conservation laws. This well-known fact in the context of General Relativity is also valid for gravitational theories which go beyond Einstein's theory. Here we derive the equations of motion for test bodies for a very large class of gravitational theories with a general nonminimal coupling to matter. These equations form the basis for future systematic tests of alternative gravity theories. Our treatment is covariant and generalizes the classic Mathisson-Papapetrou-Dixon result for spinning (extended) test bodies. The equations of …
If general relativity is the correct theory of physics on large scales, then there is a differential equation that relates the Hubble expansion function, inferred from measurements of angular diameter distance and luminosity distance, to the growth rate of large scale structure. For a dark energy fluid without couplings or an unusual sound speed, deviations from this consistency relationship could be the signature of modified gravity on cosmological scales. We propose a procedure based on this consistency relation in order to distinguish between some dark energy models and modified gravity mod…
We analyze a possibility to probe beyond-Riemann gravity (BRG) contributions, introduced by Kostelecky and Li (see Phys. Rev. D 103, 024059 (2021) and Phys. Rev. D 104, 044054 (2021)) on the basis of the Effective Field Theory (EFT) by Kostelecky Phys. Rev. D 69, 105009 (2004). We carry out such an analysis by calculating the BRG contributions to the transition frequencies of the quantum gravitational states of ultracold neutrons (UCNs). These states are being used for a test of interactions beyond the Standard Model (SM) and General Relativity (GR) in the qBOUNCE experiments. We improve by or…
I review recent results obtained for extensions of general relativity formulated within the Palatini formalism, an approach in which metric and connection are treated as independent geometrical entities. The peculiar dynamics of these theories, governed by second-order equations and having no new degrees of freedom, makes them specially suitable to address certain aspects of quantum gravity phenomenology, construct nonsingular bouncing cosmologies, and explore black hole interiors, which in the Reissner-Nordstrom case develop a compact core of finite density instead of a point-like singularity…
We investigate the asymptotic safety conjecture for quantum gravity including curvature invariants beyond Ricci scalars. Our strategy is put to work for families of gravitational actions which depend on functions of the Ricci scalar, the Ricci tensor, and products thereof. Combining functional renormalisation with high order polynomial approximations and full numerical integration we derive the renormalisation group flow for all couplings and analyse their fixed points, scaling exponents, and the fixed point effective action as a function of the background Ricci curvature. The theory is charac…
We present a theory of ghost-free massive gravity where the mass of the graviton is generated through the Brout-Englert-Higgs (BEH) mechanism and one of the four scalar fields used is that of mimetic gravity. The mass term is not of the Fierz-Pauli type and the constraint eliminates the Boulware-Deser ghost which is absent to all orders. We perform a detailed analysis using the methods of cosmological perturbation theory and consider quantum fluctuations of the degrees of freedom of massive graviton and mimetic matter. It is shown that for three of the degrees of freedom of the graviton of mas…
We review the status of tests of spacetime symmetries with gravity. Recent theoretical and experimental work has involved gravitational wave signals, precision solar-system tests, and sensitive laboratory tests searching for violations of spacetime symmetries. We present some new theoretical results relevant for short-range gravity tests, with features of multiple length scales, and possible large non-Newtonian forces at short distances.
We show that the effective field equations for a recently formulated polynomial affine model of gravity, in the sector of a torsion-free connection, accept general Einstein manifolds---with or without cosmological constant---as solutions. Moreover, the effective field equations are partially those obtained from a gravitational Yang-Mills theory known as the Stephenson-Kilmister-Yang (SKY) theory. Additionally, we find a generalisation of a minimally coupled massless scalar field in general relativity within a "minimally" coupled scalar field in this affine model. Finally, we present the road m…
A single parameter, the gravitational growth index γ, succeeds in characterizing the growth of density perturbations in the linear regime separately from the effects of the cosmic expansion. The parameter is restricted to a very narrow range for models of dark energy obeying the laws of general relativity but takes on distinctly different values in models of beyond-Einstein gravity. In analogy to the parameterized post-Newtonian (PPN) formalism for testing gravity, we extend and motivate the gravitational growth index, or Minimal Modified Gravity, approach to parameterizing beyond-Einstein cos…
