General relativity has two fundamental problems that render it unsuitable for tackling the gravitational field's quantization. The first problem is the lack of a genuine gravitational variable representing gravitation only, inertial forces apart. The second problem is its incompatibility with quantum mechanics, a problem inherited from the more fundamental conflict of special relativity with quantum mechanics. A procedure to overcome these difficulties is outlined, which amounts to replacing general relativity with its teleparallel equivalent and the Poincaré-invariant special relativity with the de Sitter-invariant special relativity. Those replacements give rise to the de Sitter-modified teleparallel gravity, which does not have the two mentioned problems. It can thus be considered an improved alternative approach to quantum gravity.
The choice of the regularization scheme in Loop Quantum Cosmology (LQC) is crucial for the predicted phenomenology. We outline how the improved scheme can be naturally realized in Quantum Reduced Loop Gravity, describing the Universe as an ensemble of microstates labeled by different graphs. The new effective dynamics presents corrections to LQC, which do not significantly affect the bouncing scenario for the most relevant kinds of matter fields in cosmology $(w \leq 1)$.
Improvement of the classical gravity with the running gravitational coupling obtained from asymptotically safe gravity, is a good way of considering the effects of quantum gravity. This is usually done for metric theories of gravity. Here we investigate the effects of such an improvement for pure affine theories of gravity. To motivate the approach, we first consider the effects of quantum improvement on the connection using metric theory and investigate the effects on the causal structure of black hole solution. Next in the framework of Schrödinger-Eddington affine theory, the general way of …
As an extension of previous works on classical tests of Kaluza-Klein (KK) gravity and as an attempt to find more stringent constraints on this theory, its effects on physical experiments and astronomical observations conducted in the Solar System are studied. We investigate the gravitational time delay at inferior conjunction caused by KK gravity, and use new Solar System ephemerides and the observation of \textit{Cassini} to strengthen constraints on KK gravity by up to two orders of magnitude. These improved upper bounds mean that the fifth-dimensional space in the soliton case is a very fla…
Usually, General Relativity (GR) is known to be unrenormalizable perturbatively from the viewpoint of quantum field theory. But in the modern sense of renormalizability, there still remains the possibility to investigate whether GR is "nonpertubatively" renormalizable or not. Here I review the basics and results in this topic based on the "Effective Average Action" approach which was proposed by M.Reuter, and discuss its application to the balck hole geometry.
Gravitational wave observations of compact binaries allow us to test general relativity (and modifications thereof) in the strong and highly-dynamical field regime of gravity. Here we confront two extensions to general relativity, dynamical Chern-Simons and Einstein-dilaton-Gauss-Bonnet theories, against the gravitational wave sources from the GWTC-1 and GWTC-2 catalogs by the LIGO-Virgo Collaboration. By stacking the posterior of individual events, we strengthen the constraint on the square root of the coupling parameter in Einstein-dilaton-Gauss-Bonnet gravity to $\sqrt{α_{\rm \tiny EdGB}} <…
Motivated by a special consideration in quantum measurement, we present a new improved energy-momentum tensor. The new tensor differs from the traditional canonical and symmetric ones, and can be derived as Nother current from a Lagrangian with second derivative. We also attempt to construct a gravitational coupling in such a way that the new energy-momentum tensor becomes the source of the gravitational field. The theory we obtain is of an Einstein-Cartan type, but derived from a minimal coupling of a Lagrangian with second-derivative, and leads to additional interaction between torsion and m…
Thermodynamical properties of black holes in gravitational theories without Local Lorentz invariance have been subject to intense investigation in the past years due to the presence of universal horizons, which are strong causal barriers even for superluminal signals. Here we present a novel general method for deriving the Smarr formula for this class of theories: in particular we show that the Smarr formulae for Einstein-Aether theory and infrared Horava gravity follow from scale invariance. We not only reproduce straightforwardly previous findings for static black hole solutions, but we are …
We derive the field equations for topologically massive gravity coupled with the most general quadratic curvature terms using the language of exterior differential forms and a first order constrained variational principle. We find variational field equations both in the presence and absence of torsion. We then show that spaces of constant negative curvature (i.e. the anti de-Sitter space $AdS_3$) and constant torsion provide exact solutions.
We continue our investigation of an improved quantization scheme for spherically symmetric loop quantum gravity. We find that in the region where the black hole singularity appears in the classical theory, the quantum theory contains semi-classical states that approximate general relativity coupled to an effective anisotropic fluid. The singularity is eliminated and the space-time can be continued into a white hole space-time. This is similar to previously considered scenarios based on a loop quantum gravity quantization.
We consider the notion of improved and perfect actions within Regge calculus. These actions are constructed in such a way that they - although being defined on a triangulation - reproduce the continuum dynamics exactly, and therefore capture the gauge symmetries of General Relativity. We construct the perfect action in three dimensions with cosmological constant, and in four dimensions for one simplex. We conclude with a discussion about Regge Calculus with curved simplices, which arises naturally in this context.
Theories such as massive Galileons and massive gravity can satisfy the presently known improved positivity bounds provided they are weakly coupled. We discuss the form of the EFT Lagrangian for a weakly coupled UV completion of massive gravity which closely parallels the massive Galileon, and perform the power counting of corrections to the scattering amplitude and the positivity bounds. The Vainshtein mechanism which is central to the phenomenological viability of massive gravity is entirely consistent with weak coupling since it is classical in nature. We highlight that the only implication …
We study the "improved dynamics" for the treatment of spherically symmetric space-times in loop quantum gravity introduced by Chiou {\em et al.} in analogy with the one that has been constructed by Ashtekar, Pawlowski and Singh for the homogeneous space-times. In this dynamics the polymerization parameter is a well motivated function of the dynamical variables, reflecting the fact that the quantum of area depends on them. Contrary to the homogeneous case, its implementation does not trigger undesirable physical properties. We identify semiclassical physical states in the quantum theory and der…
Minimum information quantum gravity (MIQG) is a theory of quantum gravity which requires no explicit microscopic quantum structure. In this article, it is shown that the MIQG action can be derived using a more elegant and straight-forward method than in the first existence proof. The required assumptions are dramatically reduced. In particular, former assumptions referring to the existence of quantum boxes, the exact differential of the entropy variation and the role of the boundary can be omitted. Moreover, the open problem of the quantum occupation number per box is solved. Thus, the argumen…
We propose a new derivation from the full Loop Quantum Gravity (LQG) to the Loop Quantum Cosmology (LQC) improved $\barμ$-scheme effective dynamics, based on the reduced phase space formulation of LQG and a proposal of effective Hamiltonian/action in the full LQG. A key step of our program is an improved regularization of the full LQG Hamiltonian on a cubic lattice. The improved Hamiltonian uses a set of "dressed holonomies" $h_Δ(\mathfrak{s})$ which not only depend on the connection $A$ but also depend on the length of the curve $\mathfrak{s}$. With the improved Hamiltonian, we propose a quan…
Recent gravitational wave observations have allowed stringent new constraints on modifications to General Relativity (GR) in the extreme gravity regime. Although these observations were consistent with compact binaries with no orbital eccentricity, gravitational waves emitted in mildly eccentric binaries may be observed once detectors reach their design sensitivity. In this paper, we study the effect of eccentricity in gravitational wave constraints of modified gravity, focusing on Jordan-Brans- Dicke-Fierz theory as an example. Using the stationary phase approximation and the post-circular ap…
This article summarizes a new approach to quantum gravity based on the concepts of modular spacetime, Born geometry, and metastring theory and their applications to quantum gravity phenomenology. In particular, we discuss a new understanding of dark matter in terms of metaparticles (zero modes of the metastring) and its relation to dark energy (the curvature of dual spacetime) in view of the actual astronomical observations.
The semiclassical approach to quantum gravity would yield the Schroedinger formalism for the wave function of metric perturbations or gravitons plus quantum gravity correcting terms in pure gravity; thus, in the inflationary scenario, we should expect correcting effects to the relic graviton (Zel'dovich) spectrum of the order (H/mPl)^2.
It is shown that if a metric in quantum gravity can be decomposed as a sum of classical and quantum parts then Einstein quantum gravity looks approximately like modified gravity with a nonminimal interaction between gravity and matter.
The improved description of the planets' interior is provided. We examine the modified gravity effects on the Earth-like planets composed of the iron core and silicate mantle. We confirm that the mass-radius relations, as well as density profiles, differ with respect to the commonly adopted Newtonian models.
Quantum-reduced loop gravity is a model of loop quantum gravity, which - from the technical point of view - is characterized by the remarkably simple form of its basic operators. In this article we examine the operators of the quantum-reduced model from the perspective of full loop quantum gravity. We show that, in spite of their simplicity, the operators of the quantum-reduced model are simply the operators of the full theory acting on states in the Hilbert space of the quantum-reduced model. The passage from the full theory operators to the "reduced" operators simply consists of noting that …
Matter and quasi-matter bounce scenarios are studied for an F(R) gravity model with holonomy corrections and a Lagrange multiplier, with a scale factor $a(t) = \left(a_0t^2 + 1 \right)^n$, where the Hubble parameter squared has a linear and a quadratic dependence on the effective energy density. Provided $n < 1/2$, it is shown that the primordial curvature perturbations are generated deeply into the contracting era, at large negative time, which makes the low-curvature limit a good approximation for calculating the perturbation power spectrum. Moreover, it is shown that, for $n$ within this ra…
Quantum gravity remains an elusive theory, in spite of our thorough understanding of the quantum theory and the general theory of relativity separately, presumably due to the lack of any observational clues. We argue that the theory of quantum gravity has a strong constraining anchor in the sector of gravitational radiation ensuring reliable physical clues, albeit in a limited observable form. In particular, all types of gravitational waves expected to be observable in LIGO-like advanced detectors are fully quantum mechanical states of radiation. Exact equivalence of the full quantum gravity t…
The incompatibility between GR and QM is generally seen as a sufficient motivation for the development of a theory of Quantum Gravity. If - so a typical argumentation - QM gives a universally valid basis for the description of all natural systems, then the gravitational field should have quantum properties. Together with the arguments against semi-classical theories of gravity, this leads to a strategy which takes a quantization of GR as the natural avenue to Quantum Gravity. And a quantization of the gravitational field would in some sense correspond to a quantization of geometry. Spacetime w…
A experimental test based on the inverse Compton effect (photon-electron collision) is proposed to check the Kinetic Quantum Gravity Theory. The experimental set-up point out a possible propulsionsystem, based on gravity control.
We have investigated the problem of traversability of wormholes in the framework of quantum improvement of gravity theory arising from functional renormalization group methods to describe the asymptotic safe quantum gravity. We have shown that improved pseudospherical wormholes could be traversable with non--exotic matter, while spherical ones could not. This is done within a specific model of improvement.
A sketch of the affine quantum gravity program illustrates a different perspective on several difficult issues of principle: metric positivity; quantum anomalies; and nonrenormalizability.
This is my Thèse d'Habilitation (HDR) on the topic of spinfoam models for quantum gravity, which I presented in l'Ecole Normale Supérieure de Lyon on december 16 2010. The spinfoam framework is a proposal for a regularized path integral for quantum gravity, inspired from Topological Quantum Field Theory (TQFT) and state-sum models. It can also be seen as defining transition amplitudes for the quantum states of geometry for Loop Quantum Gravity (LQG).
Time plays different roles in quantum mechanics and gravity. These roles are examined and the problems that the conflict in the roles presents for quantum gravity are briefly summarised.
Some relations of the quantum potential to Weyl geometry are indicated with applications to the Friedmann equations for a toy quantum cosmology. Osmotic velocity and pressure are briefly discussed in terms of quantum mechanics and superfluids with connections to gravity.
We review the relation between Loop Quantum Gravity on a fixed graph and discrete models of gravity. We compare Regge and twisted geometries, and discuss discrete actions based on twisted geometries and on the discretization of the Plebanski action. We discuss the role of discrete geometries in the spin foam formalism, with particular attention to the definition of the simplicity constraints.
Spherically symmetric gravity in Ashtekar variables coupled to Yang-Mills theory in two dimensions and its relation to dilaton gravity and Poisson sigma models are discussed. After introducing its loop quantization, quantum corrections for inverse triad components are shown to provide a consistent deformation without anomalies. The relation to Poisson sigma models provides a covariant action principle of the quantum corrected theory with effective couplings. Results are also used to provide loop quantizations of spherically symmetric models in arbitrary D space-time dimensions.
This paper reviews the histories approach to quantum mechanics. This discussion is then applied to theories of quantum gravity. It is argued that some of the quantum histories must approximate (in a suitable sense) to classical histories, if the correct classical regime is to be recovered. This observation has significance for the formulation of new theories (such as quantum gravity theories) as it puts a constraint on the kinematics, if the quantum/classical correspondence principle is to be preserved. Consequences for quantum gravity, particularly for Lorentz symmetry and the idea of "emerge…
This paper reviews the construction of quantum field theory on a 4-dimensional spacetime by combinatorial methods, and discusses the recent developments in the direction of a combinatorial construction of quantum gravity.
In this paper we have investigated the pure quantum solutions of Bohmian quantum gravity. By pure quantum solution we mean a solution in which the quantum potential cannot be ignored with respect to the classical potential, especially in Bohmian quantum gravity we are interested in the case where these two potentials are equal in their magnitude and in fact their sum is zero. Such a solutions are obtained both using the perturbation and using the linear field approximation.
A spontaneous symmetry breaking mechanism is used in quantum gravity to obtain a convergent positive definite density-matrix as the most general quantum state of Euclidean wormholes
Quantum Reduced Loop Gravity is a promising framework for linking Loop Quantum Gravity and the effective semiclassical dynamics of Loop Quantum Cosmology. We review its basic achievements and its main perspectives, outlining how it provides a quantum description of the Universe in terms of a cuboidal graph which constitutes the proper framework for applying loop techniques in a cosmological setting.
A method to evaluate spin networks for (2+1)-dimensional quantum gravity is given. We analyse the evaluation of spin networks for Lorentzian, Euclidean and a new limiting case of Newtonian quantum gravity. Particular attention is paid to the tetrahedron and to the study of its asymptotics. Moreover, we propose that all this technique can be extended to spin networks for quantum gravity in any dimension.
In this paper, we analyze the holographic principle using loop quantum gravity (LQG). This will be done by using polymeric quantization for analysing the Yurtsever's holographic bound on the entropy, which is obtained from local quantum field theories. As the polymeric quantization is the characteristic feature of loop quantum gravity, we will argue that this calculation will indicate the effect of loop quantum gravity on the holographic principle. Thus, we will be able to explicitly demonstrate the violation of the holographic principle in the loop quantum gravity.
I propose the Langevin equation for 3-geometries in the Ashtekar's formalism to describe 4D Euclidean quantum gravity, in the sense that the corresponding Fokker-Planck hamiltonian recovers the hamiltonian in 4D quantum gravity exactly. The stochastic time corresponds to the Euclidean time in the gauge, N=1 and $N^i=0$. In this approach, the time evolution in 4D quantum gravity is understood as a stochastic process where the quantum fluctuation of ` ` triad \rq\rq is characterized by the curvature at the one unit time step before. The lattice regularization of 4D quantum gravity is presented i…
External gravitational fields induce phase factors in the wave functions of particles. The phases are exact to first order in the background gravitational field, are manifestly covariant and gauge invariant and provide a useful tool for the study of spin-gravity coupling and of the optics of particles in gravitational or inertial fields. We discuss the role that spin-gravity coupling plays in particular problems.
When it comes to searches for extensions to general relativity, large efforts are being dedicated to accurate predictions for the power spectrum of density perturbations. While this observable is known to be sensitive to the gravitational theory, its efficiency as a diagnostic for gravity is significantly reduced when Solar System constraints are strictly adhered to. We show that this problem can be overcome by studying weigthed density fields. We propose a transformation of the density field for which the impact of modified gravity on the power spectrum can be increased by more than a factor …
We give a brief account of the description of the standard model in noncommutative geometry as well as the thermal time hypothesis, questioning their relevance for quantum gravity.
We discuss the meaning of background independence in quantum theories of gravity where geometry and gravity are emergent and illustrate the possibilities using the framework of quantum causal histories.
A first step towards implementing a notion of coarse graining in an intrinsically Lorentzian, discrete quantum- gravity approach, namely causal set quantum gravity is taken. It makes use of an abstract notion of scale, based on counting the number of discrete elements. To that end, the space of actions for causal set quantum gravity is written in a matrix-model-like language, and a flow equation for the effective action of the model is derived from the path integral.
A state sum model based on the group SU(1,1) is defined. Investigations of its geometry and asymptotics suggest it is a good candidate for modelling (2+1) Lorentzian quantum gravity.
In this article we give a systematic definition of the recently introduced spin foam models for four dimensional quantum gravity reviewing the main results on their semiclassical limit on fixed discretizations.
In this article a description is given of the measure in Euclidean path-integral in quantum gravity, and recent results using the Faddeev-Popov method of gauge fixing. The results suggest that the effective action is finite and positive.
The quantization of the Hamiltonian for a scalar field is performed in the framework of Quantum Reduced Loop Gravity. We outline how the regularization can be performed by using the analogous tools adopted in full Loop Quantum Gravity and the matrix elements of the resulting operator between basis states are analytic coefficients. These achievements open the way for a consistent analysis of the Quantum Gravity corrections to the classical dynamics of gravity in the presence of a scalar field in a cosmological setting.
Modified dispersion relations(MDRs) as a manifestation of Lorentz invariance violation, have been appeared in alternative approaches to quantum gravity problem. Loop quantum gravity is one of these approaches which evidently requires modification of dispersion relations. These MDRs will affect the usual formulation of the Compton effect. The purpose of this paper is to incorporate the effects of loop quantum gravity MDRs on the formulation of Compton scattering. Using limitations imposed on MDRs parameters from Ultra High Energy Cosmic Rays(UHECR), we estimate the quantum gravity-induced wavel…
The questions I have been asked during the 5th International School on Field Theory and Gravitation, have compelled me to give an account of the premises that I consider important for a beginner's approach to Loop Quantum Gravity. After a description of some general arguments and an introduction to the canonical theory of gravity, I review the background independent approach to quantum gravity, giving only a brief survey of Loop Quantum Gravity.
We elaborate the recently introduced asymptotically exact semiclassical quantum gravity derived from the Wheeler-DeWitt equation by finding a particular coherent state representation of a quantum scalar field in which the back-reaction of the scalar field Hamiltonian exactly gives rise to the classical one. In this coherent state representation classical spacetime emerges naturally from semiclassical quantum gravity.
I shall discuss some "conditions of possibility" of a quantum theory of gravity, stressing the need for solutions to some of fundamental problems confronting any attempt to apply some method of quantization to the field equations of general relativity.
This submission to the Proceedings of the Seventh Marcel-Grossman Conference is an advertisement for the use of the ``spectral analysis inner product" for minisuperspace models in quantum gravity.
