Metastable states decay at zero temperature through quantum tunneling at an exponentially small rate, which depends on the Coleman-de Luccia instanton, also known as bounce. In some theories, the bounce may not exist or its on-shell action may be ill-defined or infinite, thus hindering the vacuum decay process. In this paper, we test this possibility in modified theories of gravity interacting with a real scalar field. We consider an Einstein-Hilbert term with a non-minimally coupled scalar field and a quadratic Ricci scalar contribution. To tackle the problem we use a new analytic method, with which we prove that the scalar field on the bounce has a universal behaviour at large Euclidean radii, almost independently of the potential. Our main result is that the quadratic Ricci scalar prevents the decay, regardless of the other terms in the action.
It is shown that when a strong electric field is turned on as a background in a charged scalar field, the vacuum state of the scalar field becomes exponentially amplified. This is an analogue to gravity induced vacuum amplification, where the vacuum state becomes exponentially amplified for some geometries.
The source theory provides a straightforward way to obtain the Newton's potential upon establishing the vacuum-to-vacuum transition amplitude in quantized Einstein theory of gravity. Here, we use the same method to derive the gravitational potential of two static point masses in $f(R)=R+aR^2$ gravity.
Spherically symmetric static vacuum solutions have been built in $f(T)$ models of gravity theory. We apply some conditions on the metric components; then the new vacuum spherically symmetric solutions are obtained. Also, by extracting metric coefficients we determine the analytical form of $f(T)$.
Topologically non-trivial vacuum structure in gravity models with Cartan variables (vielbein and contortion) is considered. We study the possibility of vacuum space-time tunneling in Einstein gravity assuming that the vielbein may play a fundamental role in quantum gravitational phenomena. It has been shown that in the case of RP3 space topology the tunneling between non-trivial topological vacuums can be realized by means of Eguchi-Hanson gravitational instanton. In Riemann-Cartan geometric approach to quantum gravity the vacuum tunneling can be provided by means of contortion quantum fluctua…
We construct an n-dimensional Born-Infeld type gravity theory that has the same properties as Einstein's gravity in terms of the vacuum and particle content: Namely, the theory has a unique viable vacuum (maximally symmetric solution) and a single massless unitary spin-2 graviton about this vacuum. The BI gravity, in some sense, is the most natural, minimal generalization of Einstein's gravity with a better UV behavior, and hence, is a potentially viable proposal for low energy quantum gravity. The Gauss-Bonnet combination plays a non-trivial role in the construction of the theory. As an extre…
In linearized quantum gravity, a shift of the average energy-momentum can be compensated by a shift of the average gravitational field. This allows a renormalization scheme that naturally removes the contribution of quantum vacuum fluctuations to the cosmological constant, solving the old cosmological-constant problem for weak gravitational fields.
False vacuum decay in field theory may be formulated as a boundary value problem in Euclidean space. In a previous work, we studied its solution in single scalar field theories with quadratic gravity and used it to find obstructions to vacuum decay. For simplicity, we focused on massless scalar fields and false vacua with a flat geometry. In this paper, we generalize those findings to massive scalar fields with the same gravitational interactions, namely an Einstein-Hilbert term, a quadratic Ricci scalar, and a non-minimal coupling. We find that the scalar field reaches its asymptotic value fa…
We discuss the relevance of quantum gravity to the frontier questions in high energy phenomenology: the problems of dark matter, dark energy, and vacuum selection as well as the problems of emergent spacetime and wormholes. Dark matter and dark energy phenomenology, and the problem of vacuum selection are discussed within the context of string theory as a model of quantum gravity. Emergent spacetime and wormholes are discussed in a more general context of effective theories of quantum gravity.
A 2D symmetric teleparallel gravity model is given by a generic 4-parameter action that is quadratic in the non-metricity tensor. Variational field equations are derived. A class of conformally flat solutions is given. We also discuss static and cosmological solutions.
The Israel equations for thin shells in General Relativity are derived directly from the least action principle. The method is elaborated for obtaining the equations for double layers in quadratic gravity from the least action principle.
Recently the Petrov type I condition is introduced to reduce the degrees of freedom in the extrinsic curvature of a timelike hypersurface to the degrees of freedom in the dual Rindler fluid in Einstein gravity. In this paper we show that the Petrov type I condition holds for the solutions of vacuum Einstein-Gauss-Bonnet gravity up to the second order in the relativistic hydrodynamic expansion. On the other hand, if imposing the Petrov type I condition and Hamiltonian constraint on a finite cutoff hypersurface, the stress tensor of the relativistic Rindler fluid in vacuum Einstein-Gauss-Bonnet …
We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity. A subset of the solutions change the asymptotic structure of the anti-de Sitter space due to their logarithmic behavior.
In this presentation, we discuss the nucleation and subsequent evolution of false vacuum bubbles in the scalar-tensor gravity. First, we transform the scalar-tensor type theory of gravity to the standard Brans-Dicke type. Second, we transform the Brans-Dicke type theory from the Jordan frame to the Einstein frame. For a certain potential, a true vacuum bubble in the Einstein frame can be transformed to a false vacuum bubble in the Jordan frame by a conformal transformation. Thus, in the Jordan frame, the nucleation of a false vacuum bubble can be possible and its subsequent evolution can be de…
We present a simplified formulation of massive gravity where the Higgs fields have quadratic kinetic term. This new formulation allows us to prove in a very explicit way that all massive gravity theories considered so far inevitably have Boulware-Deser ghost in non-trivial fluctuations of background metric.
Spacetimes, which are representations of a bridge-like geometry in gravity theory, are constructed as vacuum solutions to the first order equations of motion. Each such configuration consists of two copies of an asymptotically flat sheet, connected by a bridge of finite extension where tetrad is noninvertible. These solutions can be classified into static and non-static spacetimes. The associated SO(3,1) invariant fields, namely the metric, affine connection and field-strength tensor, are all continuous across the hypersurfaces connecting the invertible and noninvertible phases of tetrad and a…
This short note is devoted to the Hamiltonian analysis of the normalized general relativity and recently proposed model of vacuum energy sequestering. The common property of these models is the presence of the global variables. We discuss the meaning of these global variables in the context of the canonical formalism and argue that their presence lead to the non-local form of the Hamiltonian constraint.
We propose a new solution to the cosmological constant problem building on a nonperturbative quantum theory of gravity with torsional instantons. These pseudoparticles, which were recently found to exist in a first order formulation of Giddings-Strominger axionic gravity, carry nontrivial Nieh-Yan topological charge. The nonperturbative ground state as generated due to tunneling effects is shown to be stable under quantum fluctuations. Within this framework, the associated vacuum angle, namely the Barbero-Immirzi topological parameter, gets fixed to a numerical value determined by the Hubble c…
Partial results are obtained for Schwarzschild- like solutions in a gravity theory with action density (-g)^(1/2)[Rik^2+bR^2]. A seven parameter family of implicit solutions is found. A number of explicit solutions are also exhibited.
General properties of vacuum solutions of $f(R)$ gravity are obtained by the condition that the divergence of the Weyl tensor is zero and $f''\neq 0$. Specifically, a theorem states that the gradient of the curvature scalar, $\nabla R$, is an eigenvector of the Ricci tensor and, if it is time-like, the space-time is a Generalized Friedman-Robertson-Walker metric; in dimension four, it is Friedman-Robertson-Walker.
In this note, I describe an attempt to construct a phenomenological gravitational model at the boundary of the AdS manifold from the variation of boundary terms in the gravitational action. I find that for an AdS vacuum in the bulk, geometric constraints require that the energy-momentum tensor has constant trace.
We study gravity coupled to a scalar field in spherical symmetry using loop quantum gravity techniques. Since this model has local degrees of freedom, one has to face ``the problem of dynamics'', that is, diffeomorphism and Hamiltonian constraints that do not form a Lie algebra. We tackle the problem using the ``uniform discretization'' technique. We study the expectation value of the master constraint and argue that among the states that minimize the master constraint is one that incorporates the usual Fock vacuum for the matter content of the theory.
We compute the vacuum energy of three-dimensional asymptotically flat space based on a Chern-Simons formulation for the Poincare group. The equivalent action is nothing but the Einstein-Hilbert term in the bulk plus half of the Gibbons-Hawking term at the boundary. The derivation is based on the evaluation of the Noether charges in the vacuum. We obtain that the vacuum energy of this space has the same value as the one of the asymptotically flat limit of three-dimensional anti-de Sitter space.
The presence of Nambu-Goldstone bosons introduce a natural degeneracy inside the vacuum solutions of the non-linear formulations of massive gravity in the same spirit of the $σ$-models. When the gravitational effects are taken into account, and the observers are located at any distance with respect to the source, this degeneracy corresponds to a multiplicity (flow) of the fundamental scales of the theory. The different values of the fundamental scales are connected each other through the broken generators of the theory.
We continue our study of gravity described by the action density (-g)^(1/2)(R_ik^2+bR^2); and look for cosmological solutions of gravity coupled to dust, for the closed isotropic model. There is a solution that at t approaches zero has for the radius, a(t)=t/3^(1/2); in the absence of dust this solution holds for all time.
Perturbative solutions to the fourth-order gravity describing spherically-symmetric, static and electrically charged black hole in an asymptotically de Sitter universe is constructed and discussed. Special emphasis is put on the lukewarm configurations, in which the temperature of the event horizon equals the temperature of the cosmological horizon.
The Hawking radiation of static, spherically symmetric, asymptotically flat solutions in quadratic gravity, is here explored. The emitted fermions are governed by the Dirac equation in the generalized uncertainty principle (GUP) context, that probes the spacetime (quantum) nature. The Hawking thermal spectrum is scrutinized out of the tunnelling method and the WKB procedure. The Hawking flux is shown to vanish for small black holes, for a precise combination of the GUP parameter and the coupling constants that drive the gravitational interaction in quadratic gravity, yielding absolutely stable…
More than three decades ago quadratic gravity was found to present a perturbative, renormalizable and asymptotically free theory of quantum gravity. Unfortunately the theory appeared to have problems with a spin-2 ghost. In this essay we revisit quadratic gravity in a different light by considering the case that the asymptotically free interaction flows to a strongly interacting regime. This occurs when the coefficient of the Einstein-Hilbert term is smaller than the scale $Λ_{\mathrm{QG}}$ where the quadratic couplings grow strong. Here QCD provides some useful insights. By pushing the analog…
In this paper we have considered a red-shift based linear correction in derivative of action in the context of vacuum $f(R)$ gravity. Here we have found out that the linear correction may describe the late time acceleration which is appeared by SNeIa with no need of dark energy. Also we have calculated the asymptotic action for the desired correction. The value of all solutions may reduce to de' Sitter universe in the absence of correction term.
We show that Schwarzschild geometry remains as a vacuum solution for those four-dimensional f(T) gravitational theories behaving as ultraviolet deformations of general relativity. In the gentler context of three-dimensional gravity, we also find that the infrared-deformed f(T) gravities, like the ones used to describe the late cosmic speed up of the Universe, have as the circularly symmetric vacuum solution a Deser-de Sitter or a BTZ-like spacetime with an effective cosmological constant depending on the infrared scale present in the function f(T).
We review a long-standing difficulty in some semiclassical models of vacuum and vacuum decay. Surprisingly enough these models, careless of their transparent formulation, are affected by, both, technical and conceptual issues. After proving some general results that are relevant for, both, the Euclidean and Lorentzian sectors of their dynamics, we briefly highlight their importance in connection with the issues discussed before, arguing that their solution might be interesting in our quest for quantum gravity.
We present a systematic procedure of finding the shock wave equation in anisotropic spacetime of quadratic gravity with Lagrangian ${\cal L}=R+ Λ+αR_{μνσρ}R^{μνσρ}+βR_{μν}R^{μν}+γR^2+{\cal L}_{\rm matter}$. The general formula of the butterfly velocity is derived. We show that the shock wave equation in the planar, spherical or hyperbolic black hole spacetime of Einstein-Gauss-Bonnet gravity is the same as that in Einstein gravity if space is isotropic. We consider the modified AdS spacetime deformed by the leading correction of the quadratic curvatures and find that the fourth order derivativ…
We construct new solutions of five-dimensional quadratic gravity as direct products of a constant curvature two-surface with a solution of three-dimensional new massive gravity with constant scalar curvature. These solutions could represent near-horizon limits of five-dimensional asymptotically flat black strings or black rings. A number of these non-asymptotically flat solutions are themselves black strings or rings. A by-product of our analysis is the construction of new solutions of four-dimensional quadratic gravity obtained by toroidal reduction of the five-dimensional solutions with flat…
We study gravitational waves generated during the inflationary epoch in presence of a decaying cosmological parameter on a 5D geometrical background which is Riemann flat. Two examples are considered, one with a constant cosmological parameter and the second with a decreasing one.
The quadratic gravity constraints are reformulated in terms of the Newman-Penrose-like quantities. In such a frame language, the field equations represent a linear algebraic system for the Ricci tensor components. In principle, a procedure for the combination of the Ricci components with standard geometric identities can be applied in a similar way as in the case of general relativity. These results could serve in various subsequent analyses and physical interpretations of admitted solutions to quadratic gravity. Here, we demonstrate the utility of such an approach by explicitly proving genera…
In the Wheeler-DeWitt framework, by a gauge fixing procedure, we set up a scheme to recover a Schrödinger type equation, living in the orbits space with the {\it lapse} function as evolution parameter. By means of the associated stationary equation, we have the possibility of calculating quantum corrections to classical quantities. The Schwarzschild wormhole case is discussed as an example of application.
In this paper we investigate spherically symmetric vacuum solutions of $f(R)$ gravity in a higher dimensional spacetime. With this objective we construct a system of non-linear differential equations, whose solutions depend on the explicit form assumed for the function $F(R)=\frac{df(R)}{dR}$. We explicit show that for specific classes of this function exact solutions from the field equations are obtained; also we find approximated results for the metric tensor for more general cases admitting $F(R)$ close to the unity.
We explore a background-independent theory of composite gravity. The vacuum expectation value of the composite metric satisfies Einstein's equations (with corrections) as a consistency condition, and selects the vacuum spacetime. A gravitational interaction then emerges in vacuum correlation functions. The action remains diffeomorphism invariant even as perturbation theory is organized about the dynamically selected vacuum spacetime. We discuss the role of nondynamical clock and rod fields in the analysis, the identification of physical observables, and the generalization to other theories inc…
In this paper the Seiberg-Witten map is first analyzed for non-commutative Yang-Mills theories with the related methods, developed in the literature, for its explicit construction, that hold for any gauge group. These are exploited to write down the second-order Seiberg-Witten map for pure gravity with a constant non-commutativity tensor. In the analysis of pure gravity when the classical space-time solves the vacuum Einstein equations, we find for three distinct vacuum solutions that the corresponding non-commutative field equations do not have solution to first order in non-commutativity, wh…
We introduce a $(5+m)$-dimensional vacuum description of five-dimensional bulk inflaton models with exponential potentials that makes analysis of cosmological perturbations simple and transparent. We show that various solutions, including the power-law inflation model recently discovered by Koyama and Takahashi, are generated from known $(5+m)$-dimensional vacuum solutions of pure gravity. We derive master equations for all types of perturbations, and each of them becomes a second order differential equation for one master variable supplemented by simple boundary conditions on the brane. One e…
Asymptotically Safe theories of gravity have recently received much attention. In this work we discuss a class of inflationary models derived from quantum-gravity modification of quadratic gravity according to the induced scaling around the non-Gaussian fixed point at very high energies. It is argued that the presence of a three dimensional ultraviolet critical surface generates operators of non-integer power of the type $R^{2-θ/2}$ in the effective Lagrangian, where $θ>0$ is a critical exponent. The requirement of a successful inflationary model in agreement with the recent Planck 2015 data p…
We investigate several quantum phenomena related to quadratic gravity after rewriting the general fourth-order action in a more convenient form that is second-order in derivatives and produces only first-class constraints in phase space. We find that a Higgs mechanism may occur in the conformally invariant subset of the general quadratic action if the theory is conformally coupled to a scalar field that acquires a non-zero vacuum expectation value and spontaneously breaks the conformal symmetry. Then, in the broken phase, the originally massless spin-2 ghost may absorb both the scalar and vect…
In this note, we evaluate the Weyl-invariant quadratic curvature tensors for the particular Weyl's gauge field constructed in the $3+1$-dimensional noncompact Weyl-Einstein-Yang-Mills model. We subsequently extend the model to its higher curvature version. Here, we also compute Weyl-invariant extension of topological Gauss-Bonnet term for this specific choice of vector field.
Standard methods for calculating the black hole entropy beyond general relativity are ambiguous when the horizon is non stationary. We fix these ambiguities in all quadratic curvature gravity theories, by demanding that the entropy be increasing at every time, for linear perturbations to a stationary black hole. Our result matches with the entropy formula found previously in holographic entanglement entropy calculations. We explicitly calculate the entropy increase for Vaidya-like solutions in Ricci-tensor gravity to show that (unlike the Wald entropy) the holographic entropy obeys a Second La…
It is shown that the notion of Conformal Mass can be defined within a given anti-de Sitter (AdS) branch of a Lovelock gravity theory as long as the corresponding vacuum is not degenerate. Indeed, conserved charges obtained by the addition of Kounterterms to the bulk action turn out to be proportional to the electric part of the Weyl tensor, when the fall-off of a generic solution in that AdS branch is considered. The factor of proportionality is the degeneracy condition for the vacua in the particular Lovelock AdS theory under study. This last feature explains the obstruction to define Conform…
In the present paper we investigate the conservative conditions in Quadratic Gravity. It is shown explicitly that the Bianchi identities lead to the conservative condition of the left-hand-side of the (gravitational) field equation. Therefore, the total energy-momentum tensor is conservative in the bulk (like in General Relativity). However, in Quadratic Gravity it is possible to have singular hupersurfaces separating the bulk regions with different behavior of the matter energy-momentum tensor or different vacua. They require special consideration. We derived the conservative conditions on su…
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…
An effective theory of gravity in the infrared is proposed, which involves the determinant of the metric relative to the determinant of a prior metric taken to be that of Minkowski spacetime. This effective theory can be interpreted as a generalization of unimodular gravity. In a cosmological context with ultrarelativistic or cold matter, the resulting field equations have only one solution, empty Minkowski spacetime (selected by the prior metric of the theory). The introduction of energy exchange between vacuum and matter gives rise to nonstatic cosmic solutions. It is found that Minkowski sp…
We use variational methods to calculate quasilocal energy quantum corrections. A comparison with the effective potential calculated at quadratic order is made by means of gaussian wave functionals. The method is a particular case of the effective action for composite operators used in quantum field theory. In pure gravity the method is applied for the first time. Implications on the foam-like scenario are discussed.
We briefly review the previous works on the renormalization group in quantum general relativity with the cosmological constant, based on the Vilkovisky and DeWitt version of effective action. On top of that, we discuss the prospects of the applications of this version of renormalization group to the cosmological models with a running Newton constant and vacuum energy density.
