Non-minimal interactions are proven to be generated at the one-loop level in simple scalar-tensor gravity models. The John interaction from the Fab Four class is generated. The interaction affects the speed of gravitational waves in the contemporary Universe. Its role in low-energy phenomenology is discussed. Brans-Dicke-like interaction is generated in a non-minimal model. An opportunity to generate a dynamic low-energy Newton constant is addressed.
We study cosmological tensor perturbations generated during de Sitter inflation in the conformal gravity with mass parameter $m^2=2H^2$. It turns out that tensor power spectrum is scale-invariant.
Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian configurations are parameterized by a scalar and a symmetric two-tensor, it is argued that, in general situat…
Constructs from conformal geometry are important in low dimensional gravity models, while in higher dimensions the higher curvature interactions of Lovelock gravity are similarly prominent. Considering conformal invariance in the context of Lovelock gravity leads to natural, higher-curvature generalizations of the Weyl, Schouten, Cotton and Bach tensors, with properties that straightforwardly extend those of their familiar counterparts. As a first application, we introduce a new set of conformally invariant gravity theories in D=4k dimensions, based on the squares of the higher curvature Weyl …
We apply a recent argument of Verlinde to loop quantum gravity, to conclude that Newton's law of gravity emerges in an appropriate limit and setting. This is possible because the relationship between area and entropy is realized in loop quantum gravity when boundaries are imposed on a quantum spacetime.
We construct, and establish the (covariant) conservation of, a 4-index "super-stress tensor" for TMG. Separately, we discuss its invalidity in quadratic curvature models and suggest a generalization.
We introduce squeezed vacua in loop quantum gravity, a new overcomplete basis of states that contain prescribable correlations between geometric operators. We study the behavior of long-range correlations and discuss the relevance of these states for the reconstruction of a semiclassical spacetime from loop quantum gravity.
We investigate whether the classical equivalence of $f(R)$ gravity and its formulation as scalar-tensor theory still holds at the quantum level. We explicitly compare the corresponding one-loop divergences and find that the equivalence is broken by off-shell quantum corrections, but recovered on-shell.
In this paper, we review some general formulations of exact renormalisation group equations and loop equations for tensor models and tensorial group field theories. We illustrate the use of these equations in the derivation of the leading order expectation values of observables in tensor models. Furthermore, we use the exact renormalisation group equations to establish a suitable scaling dimension for interactions in Abelian tensorial group field theories with a closure constraint. We also present analogues of the loop equations for tensor models.
Out of several possible extensions of general relativity, the scalar-tensor theory is the most popular for several reasons. Since the quantum description of gravity is yet to be formulated properly, the understanding of a gravitational theory remains incomplete until the study of thermodynamic and fluid-gravity aspects, which provides an alternative viewpoint to understand the gravitational theory. In this review, we study these features (thermodynamics and the fluid gravity analogy) in a rigorous and yet in a concise manner for the scalar-tensor gravity, which has been revealed in our recent …
In this contribution, classes of shear-free cosmological dust models with irrotational fluid flows will be investigated in the context of scalar-tensor theories of gravity. In particular, the integrability conditions describing a consistent evolution of the linearised field equations of quasi-Newtonian universes are presented. We also derive the covariant density and velocity propagation equations of such models and analyse the corresponding solutions to these perturbation equations.
Tensor models provide a way to access the path-integral for discretized quantum gravity in d dimensions. As in the case of matrix models for two-dimensional quantum gravity, the continuum limit can be related to a Renormalization Group fixed point in a setup where the tensor size N serves as the Renormalization Group scale. We develop functional Renormalization Group tools for tensor models with a main focus on a rank-3 model for three-dimensional quantum gravity. We rediscover the double-scaling limit and provide an estimate for the scaling exponent. Moreover, we identify two additional fixed…
In the Riemann geometry, the metric's equation of motion for an arbitrary Lagrangian is succinctly expressed in term of the first variation of the action with respect to the Riemann tensor if the Riemann tensor were independent of the metric. Let this variation be called the E-tensor. Noting that the E-tensor and equations of the motion for a general Lovelock gravity have the same differential degree, we define generalized Lovelock gravity as polynomial scalar densities constructed out from the Riemann tensor and its arbitrary covariant derivatives such that they lead to the same differential …
We calculate holographically arbitrary n-point correlators of the boundary stress tensor in three-dimensional Einstein gravity with negative or vanishing cosmological constant. We provide explicit expressions up to 5-point (connected) correlators and show consistency with the Galilean conformal field theory Ward identities and recursion relations of correlators, which we derive. This provides a novel check of flat space holography in three dimensions.
We study spherically-symmetric structures in Conformal Gravity and in a scalar-tensor extension and gain some more insight about these gravitational theories. In both cases we analyze solutions in two systems: perfect fluid solutions and boson stars of a self-interacting complex scalar field. In the purely tensorial (original) theory we find in a certain domain of parameter space finite mass solutions with a linear gravitational potential but without a Newtonian contribution. The scalar-tensor theory exhibits a very rich structure of solutions whose main properties are discussed. Among them, s…
We revisit the analogy between a minimally coupled scalar field in general relativity and a perfect fluid, correcting previous identifications of effective temperature and chemical potential. This provides a useful complementary picture for the first-order thermodynamics of scalar-tensor gravity, paving the way for the Einstein frame formulation (which eluded previous attempts) and raises interesting questions to further develop the analogy.
In this paper, we study various cosmological parameters and quantities in scalar-tensor gravity from inflation and swampland conjecture. Therefore, by selecting different models such as power-law, exponential, and logarithmic in the framework of scalar-tensor theory, we obtain potential, tensor-to-scalar ratio, and the scalar spectral index. Next, we examine new constraints and compare the corresponding results with the latest observable data. Here, we take advantage of the obtained results and determine the compatibility or incompatibility of the corresponding model with the swampland conject…
We introduce a new loop expansion that provides a resolution of the identity in the Hilbert space of loop quantum gravity on a fixed graph. We work in the bosonic representation obtained by the canonical quantization of the spinorial formalism. The resolution of the identity gives a tool for implementing the projection of states in the full bosonic representation onto the space of solutions to the Gauss and area matching constraints of loop quantum gravity. This procedure is particularly efficient in the semiclassical regime, leading to explicit expressions for the loop expansions of coherent,…
A simple argument indicates that covariant loop gravity (spinfoam theory) predicts a maximal acceleration, and hence forbids the development of curvature singularities. This supports the results obtained for cosmology and black holes using canonical methods.
Previously, the Einstein equation has been described as an equation of state, general relativity as the equilibrium state of gravity, and $f({\cal R})$ gravity as a non-equilibrium one. We apply Eckart's first order thermodynamics to the effective dissipative fluid describing scalar-tensor gravity. Surprisingly, we obtain simple expressions for the effective heat flux, "temperature of gravity", shear and bulk viscosity, and entropy density, plus a generalized Fourier law in a consistent Eckart thermodynamical picture. Well-defined notions of temperature and approach to equilibrium, missing in …
By making use of the background field method, the one-loop quantization for Euclidean Einstein-Weyl quadratic gravity model on the de Sitter universe is investigated. Using generalized zeta function regularization, the on-shell and off-shell one-loop effective actions are explicitly obtained and one-loop renormalizability, as well as the corresponding one-loop renormalization group equations, are discussed. The so called critical gravity is also considered.
We review and extend the Gauge Vectors-Tensor gravity: a covariant theory of gravity composed of a metric and gauge fields, leading to simple second order partial differential equations of motion, whose Newtonian and strong limits coincide to those of the Einsten-Hilbert action but the physics of its very weak fields should be identified through observation. We show that GVT is at least as dynamically stable as the Einstein-Hilbert gravity. It accommodates the MOND paradigm. We study its gravitational light deflection. We show that the post Newtonian parameter of $γ$ vanishes in the MOND regim…
A natural question arises from observable signatures of scalar, fermion, and vector degrees of freedom (d.o.f.) in our Universe along with spin 2 symmetric tensor field in the form of gravity: why is our Universe is free of any perceptible signature of massless antisymmetric tensor modes? This work brings out a natural explanation of these phenomena through higher curvature quantum d.o.f. in the gravity sector that were dominant in the early universe. In the backdrop of a F(R) gravity model, we propose how the scalar d.o.f. associated with higher curvature term in the model can generate a heav…
In this article we further investigate the construction of graph coherent states, first introduced in [1], in the context of loop quantum gravity. We specifically investigate the possibility of defining a family of graph coherent states adapted to the canonical loop quantum gravity Hamiltonian. After discussing various aspects of the general framework and the choice of operators, we use the Euclidean part of the Hamiltonian operator to propose a generator of the generalized canonical structure, necessary to define the coherent states. We then apply the construction procedure, leading to a new …
We present the complete set of universal one-loop beta functions of cubic gravity in six dimensions. The system admits over 8000 distinct fixed points, of which more than 200 are real. Some of them might be relevant for the quantisation of gravity in the physical case of four dimensions.
The metric-affine gravity provides a useful framework for analyzing gravitational dynamics since it treats metric tensor and affine connection as fundamentally independent variables. In this work, we show that, a metric-affine gravity theory composed of the invariants formed from non-metricity, torsion and curvature tensors can be decomposed into a theory of scalar, vector and tensor fields. These fields are natural candidates for the ones needed by various cosmological and other phenomena. Indeed, we show that the model accommodates TeVeS gravity (relativistic modified gravity theory), vector…
An exact de Sitter solution of scalar-tensor gravity is found, in which the non-minimal coupling scalar is rolling along a non-constant potential. Based on this solution, a dust-filled FRW universe is explored in frame of scalar-tensor gravity. The effective dark energy induced by the sole non-minimal scalar can be quintessence-like, phantom-like, and more significantly, can cross the phantom divide. The rich and varied properties of scalar-tensor gravity even with only one scalar is shown in this article.
We present a direct confirmation of the validity of the equivalence principle for unstructured test bodies in scalar tensor gravity. Our analysis is complementary to previous approaches and valid for a large class of scalar-tensor theories of gravitation. A covariant approach is used to derive the equations of motion in a systematic way and allows for the experimental test of scalar-tensor theories by means of extended test bodies.
Hawking has proven that black holes which are stationary as the endpoint of gravitational collapse in Brans--Dicke theory (without a potential) are no different than in general relativity. We extend this proof to the much more general class of scalar-tensor and f(R) gravity theories, without assuming any symmetries apart from stationarity.
It is proved that all thin-shell wormholes built from two identical regions of vacuum static, spherically symmetric space-times have a negative shell surface energy density in any scalar-tensor theory of gravity with a non-ghost massless scalar field and a non-ghost graviton.
We use the 1+1+2 covariant approach to clarify a number of aspects of spherically symmetric solutions of non-minimally coupled scalar tensor theories. Particular attention is focused on the extension of Birkhoff's theorem and the nature of quasi-local horizons in this context.
We consider the evolution of cosmological gravitational waves in scalar-tensor theory and $F(R)$ gravity theory as typical models of the modified gravity. Although the propagation speed is not changed from the speed of light, the propagation phase changes when we compare the propagation in these modified gravity theories with the propagation in the $Λ$CDM model. The phase change might be detected in future observations.
We work out the one-loop contribution to the lepton anomalous magnetic moment coming from Unimodular Gravity. We use Dimensional Regularization and Dimensional Reduction to carry out the computations. In either case, we find that Unimodular Gravity gives rise to the same one-loop correction as that of General Relativity.
In modified gravity, the one-loop matter power spectrum exhibits an ultraviolet divergence as shown in the framework of the degenerate higher-order scalar-tensor theory. To address this problem, we extend the effective field theory of large scale structure to modified gravity theories. We find that new counterterms appear and renormalize the ultraviolet divergence as a natural consequence of non-linearity in the modified Poisson equation. The renormalized one-loop matter power spectrum is useful to test modified gravity theories by comparing to observations.
The holographic bound has been extended to the different theory of gravities such as scalar-tensor gravity and $f(R)$ gravity according to the Noether charge definition of the entropy for a black hole surface. We have introduced some popular examples of the flat FRW cosmology in order to investigate holographic bound in scalar-tensor and $f(R)$ gravity. Using the holographic bound, we put an additional constraint on the scalar-tensor gravity and $f(R)$ gravity parameters. We also discuss about the transformation from Jordan frame to Einstein frame.
We present a construction of kinematic quantum states for theories of tensor fields of an arbitrary sort. The construction is based on projective techniques by Kijowski. Applying projective quantum states for Loop Quantum Gravity obtained by Lanery and Thiemann we construct quantum states for LQG coupled to tensor fields.
We derive the gravitational energy-momentum pseudo-tensor $τ^μ_{\phantomμν}$ in both Palatini and metric approaches to $f(R)$ gravity. We then obtain the related cosmological gravitational energy density. Considering a flat Friedmann-Lemaître-Robertson-Walker spacetime, the energy density complex of matter and gravitation vanishes in the metric approach, but results non-vanishing in the Palatini formalism. This feature could be relevant in order to physically discriminate between the two approaches.
We explore the possibility of testing modified gravity exhibiting the Vainshtein mechanism against observations of cluster lensing. We work in the most general scalar-tensor theory with second-order field equations (Horndeski's theory), and derive static and spherically symmetric solutions, for which the scalar field is screened below a certain radius. It is found that the essential structure of the problem in the most general case can be captured by the program of classifying Vainshtein solutions out of different solutions to a quintic equation, as has been performed in the context of massive…
We discuss the dynamics of extended test bodies for a large class of scalar-tensor theories of gravitation. A covariant multipolar Mathisson-Papapetrou-Dixon type of approach is used to derive the equations of motion in a systematic way for both Jordan and Einstein formulations of these theories. The results obtained provide the framework to experimentally test scalar-tensor theories by means of extended test bodies.
Loop quantum gravity is a physical theory which aims at unifying general relativity and quantum mechanics. It takes general relativity very seriously and modifies it via a quantisation. General relativity describes gravity in terms of geometry. Therefore, quantising such theory must be equivalent to quantising geometry and that is what loop quantum gravity does. This sounds like a mathematical task as well. This is why in this paper we will present the mathematics of loop quantum gravity. We will do it from a mathematician point of view. This paper is intended to be an introduction to loop qua…
