Using the cosmological perturbation theory in terms of the delta-N formalism, we find the simple formulation of the evolution of the curvature perturbation in generalized gravity theories. Compared with the standard gravity theory, a crucial difference appears in the end-boundary of the inflationary stage, which is due to the non-ideal form of the energy momentum tensor that depends explicitly on the curvature scalar. Recent study shows that ultraviolet-complete quantum theory of gravity may be approximated by using a generalized gravity action. Our paper may give an important step in understanding the evolution of the curvature perturbation during inflation, where the energy momentum tensor may not be given by the ideal form due to the corrections from the fundamental theory.
We consider extensions of General Relativity based on the non-local function $f(R, \Box^{-1} R)$, where $R$ is the Ricci curvature scalar and the non-locality is due to the term $\Box^{-1} R$. We focus on cosmological minisuperspaces and select viable models by the Noether Symmetry Approach. Then we find viable exact solutions pointing out the role of non-locality in cosmology.
We show that, in four-dimensional spacetimes with an arbitrary Einstein metric, with and without a cosmological constant, perturbative dynamical degrees of freedom in generic quadratic-curvature gravity can be decoupled into massless and massive parts. The massive part has the structure identical to, modulo the over-all sign, the non-Fierz-Pauli-type massive gravity, and a further decomposition into the spin-2 and spin-0 sectors can be done. The equivalence at the level of equations of motion allows us to translate various observational bounds on the mass of extra fields into constraints on th…
We discuss a recently proposed limiting curvature theory of gravity and its application to the problem of singularities inside black holes. In this theory the growth of the curvature is suppressed by specially chosen inequality constraints included in the gravity action. We consider a case of a spherically symmetric four dimensional black hole and demonstrated that imposed curvature constraints modify a solution in the black hole interior. Instead of forming the curvature singularity the modified metric describes a space which is exponentially expanding in one direction and oscillating the oth…
We show that Thurston geometries are solutions to a large class of 3D quadratic curvature theories, where New Massive Gravity, which was studied in arXiv:2104.00754, is a special case.
We compute curvature-dependent graviton correlation functions and couplings as well as the full curvature potential $f(R)$ in asymptotically safe quantum gravity coupled to scalars. The setup is based on a systematic vertex expansion about metric backgrounds with constant curvatures initiated in arXiv:1711.09259 for positive curvatures. We extend these results to negative curvature and investigate the influence of minimally coupled scalars. The quantum equation of motion has two solutions for all accessible numbers of scalar fields. We observe that the solution at negative curvature is a minim…
General relativity may be an effective theory with higher curvature correction terms in the action. Inclusion of these terms leads to exciting new possibilities, e.g., gravitational and electromagnetic perturbations following different geodesics; leading to a time delay. Such a time delay was observed between the gravitational wave event GW170817 and its electromagnetic counterpart GRB 170817A. We describe how this effect can be used to constrain the coupling of the higher curvature term. Our method is sufficiently general and applicable to any higher curvature theory.
The zeroth law of black hole mechanics is an assertion of constancy of the surface gravity on a stationary Killing horizon. The Hawking temperature of the black hole horizon is proportional to the surface gravity. Therefore, the constancy of the surface gravity is reminiscent of the zeroth law of ordinary thermodynamics. In this work, we provide a proof of the zeroth law in Lanczos-Lovelock theories of gravity, where the Einstein Hilbert action is supplemented by higher curvature terms.
The physical foundations for the geometric structure of relativistic theories of gravitation. From General Relativity to Extended Theories of Gravity through Ehlers-Pirani-Schild approach
In this paper we describe a model of a four-dimensional spherically symmetric black hole in a limiting curvature theory of gravity. In this theory the Einstein-Hilbert action is modified by adding to the action terms providing inequality constraints on chosen curvature invariants. We demonstrated that in such a model, instead of formation of the curvature singularity, the spacetime remains regular in the black hole interior. For black holes with gravitational radius much larger than the radius $\ell$ of the critical curvature the obtained solutions describe a space exponentially expanding in o…
By generalizing different recent works to the context of higher curvature gravity, we provide a unifying framework for three related results: (i) If an asymptotically AdS spacetime computes the entanglement entropies of ball-shaped regions in a CFT using a generalized Ryu-Takayanagi formula up to second order in state deformations around the vacuum, then the spacetime satisfies the correct gravitational equations of motion up to second order around AdS; (ii) The holographic dual of entanglement entropy in higher curvature theories of gravity is given by Wald entropy plus a particular correctio…
We construct Komar-type integrals for theories of gravity of higher order in the Riemann curvature coupled to simple kinds of matter (scalar and vector fields) and we use them to compute Smarr formulae for black-hole solutions in those theories. The equivalence between f(R) and Brans-Dicke theories is used to argue that the dimensionful parameters that appear in scalar potentials must be interpreted as thermodynamical variables ("pressures") and we give a general expression for their conjugate potentials ("volumes"}.
We provide new formulas for the energy of black hole solutions in the anti-de Sitter (AdS) sector of a generic gravity theory with curvature-squared terms. This is achieved by the addition of counterterms of the extrinsic type (\emph{Kounterterms}) which produces a finite variation of the total action. The procedure is compatible with the boundary conditions in asymptotically AdS spaces within the framework of Quadratic Curvature Gravity (QCG) theory. As a consequence, without resorting to background-substraction, or linearized methods, the conserved charges correctly reproduce the energy of s…
We discuss locally Weyl (scale) covariant generalisations of gravitational theories using Riemann-Cartan-Weyl space-times in arbitrary dimensions. We demonstrate the procedure of Weyl gauging on two examples in particular: General relativity, and topologically massive gravity in three dimensions.
We consider f(R) gravity theories in the presence of a scalar field minimally coupled to gravity with a self-interacting potential. When the scalar field backreacts to the metric we find at large distances scalarized Schwarzschild-AdS and Schwarzschild-AdS-like black hole solutions. At small distances due to strong curvature effects and the scalar dynamis we find a rich structure of scalarized black hole solutions. When the scalar field is conformally coupled to gravity we also find scalarized black hole solutions at small distances.
Building on the recently introduced notion of quantum Ricci curvature and motivated by considerations in nonperturbative quantum gravity, we advocate a new, global observable for curved metric spaces, the curvature profile. It is obtained by integrating the scale-dependent, quasi-local quantum Ricci curvature, and therefore also depends on a coarse-graining scale. To understand how the distribution of local, Gaussian curvature is reflected in the curvature profile, we compute it on a class of regular polygons with isolated conical singularities. We focus on the case of the tetrahedron, for whi…
We disprove the widespread belief that higher order curvature theories of gravity in the metric-affine formalism are generally ghost-free. This is clarified by considering a sub-class of theories constructed only with the Ricci tensor and showing that the non-projectively invariant sector propagates ghost-like degrees of freedom. We also explain how these pathologies can be avoided either by imposing a projective symmetry or additional constraints in the gravity sector. Our results put forward that higher order curvature gravity theories generally remain pathological in the metric-affine (and …
In this paper we will study the complete equations of motion for a ghost free quadratic curvature infinite derivative gravity. We will argue that within the scale of non-locality, Schwarzschild-type singular metric solution is not {\it permissible}. Therefore, Schwarzschild-type vacuum solution which is a prediction in Einstein-Hilbert gravity may {\it not} persist within the region of non-locality. We will also show that just quadratic curvature gravity, without infinite derivatives, always allows Schwarzschild-type singular metric solution.
We review the possible violation of the Equivalence Principle at finite temperature T in the framework of curvature based Extended Theories of Gravity. Specifically, we first show how it is possible to derive Equivalence Principle violation from Quantum Field Theory at non-vanishing T. Subsequently, we exhibit how this result can be precisely recovered by following an alternative path that envisages the employment of generalized Einstein equations with a temperature-dependent energy-momentum tensor. Finally, we adopt the latter formalism in the context of some Extended Gravity models to quanti…
Solving field equations in the context of higher curvature gravity theories is a formidable task. However in many situations, e.g., in the context of $f(R)$ theories the higher curvature gravity action can be written as Einstein-Hilbert action plus a scalar field action. We show that not only the action but the field equations derived from the action are also equivalent provided the spacetime is regular. We also demonstrate that such equivalence continues to hold even when gravitational field equations are projected on a lower dimensional hypersurface. We have further depicted explicit example…
We start by briefly reviewing the description of gravity theories as gauge theories in four dimensions. More specifically we recall the procedure leading to the results of General Relativity and Weyl Gravity in a gauge-theoretic manner. Then, after a brief reminder of the formulation of gauge theories on noncommutative spaces, we review our recent work, where gravity is constructed as a gauge theory on the fuzzy $dS_4$.
