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In bimetric gravity, nonbidiagonal solutions describing a static, spherically symmetric, and asymptotically flat black hole are given by a pair of Schwarzschild geometries, one in each metric sector. The two geometries are linked by a nontrivial diffeomorphism, which can be fully determined analytically if the two geometries possess the same isometries. This exact solution depends on four free parameters: the mass parameters of the two black holes, the ratio between the areal radii of the two metrics, and the proportionality constant between their (appropriately normalized) time-translation invariance Killing vector fields. We study the dynamics of axial dipolar perturbations on such a background and obtain general analytical solutions for their evolution. We show that, in general, the characteristic curves followed by dipolar gravitational waves are spacelike with respect to both metrics, and thus the propagation is superluminal. In fact, the velocity of a pulse, as measured by a static observer, turns out to increase with the distance to the black hole. The only exception to this general behavior corresponds to the special case where the two proportionality constants linking the areal radii and the Killing vectors coincide, for which waves travel at the speed of light. Therefore, we conclude that this is the only physically reasonable background, and thus our results restrict the class of viable black-hole solutions in bimetric gravity.

We study spherically symmetric spacetime perturbations induced by a neutral scalar in the near-horizon region of extreme Reissner-Nordstrom black holes. For the unperturbed black hole, the near-horizon region is given by another exact solution of the Einstein-Maxwell equations, namely the Bertotti-Robinson spacetime. Our aim is to extend this connection beyond the background level and identify perturbations of a Bertotti-Robinson spacetime as near-horizon perturbations of an extreme Reissner-Nordstrom black hole. We explain that explicit identification of the perturbative solutions to the two different backgrounds can only work in appropriate gauges. For this reason, we first solve the two perturbation problems in the most general spherically symmetric gauges and then find the necessary gauge conditions for matching the Reissner-Nordstrom and Bertotti-Robinson perturbative solutions in the near-horizon limit., Comment: 23 pages; v2: minor edits, appendix added

Different approaches to quantum gravity, such as loop quantum cosmology and group field theory, predict the resolution of the initial cosmological singularity via a bounce: a regular spacetime region that connects the expanding branch of the universe to a contracting branch. The cosmological arrow of time, which by definition points in the direction of cosmic expansion, is reversed at the bounce. Nonetheless, it is still possible to discriminate between the two branches by considering different arrows, as defined for instance by the growth of perturbations. After reviewing general aspects of the time arrow problem in cosmology, we examine the properties of different arrows of time in bouncing cosmologies, focusing on the loop quantum cosmology bounce as a case study. These issues are examined in detail for an exact solution to the effective Friedmann equations of loop quantum cosmology with pressureless dust and a cosmological constant, which is a simplified version of the $\Lambda$CDM bounce scenario., Comment: 11 pages; invited contribution to the volume "Time and Timelessness in Fundamental Physics and Cosmology" (eds. S. De Bianchi, M. Forgione and L. Marongiu), published by Springer; v2: added references, matches published version

We present a formalism to study linear perturbations of bimetric gravity on any spherically symmetric background, including dynamical spacetimes. The setup is based on the Gerlach-Sengupta formalism for general relativity. Each of the two background metrics is written as a warped product between a two-dimensional Lorentzian metric and the round metric of the two-sphere. The different perturbations are then decomposed in terms of tensor spherical harmonics, which makes the two polarity (axial and polar) sectors decouple. In addition, a covariant notation on the Lorentzian manifold is used so that all expressions are valid for any coordinates. In this theory, there are seven physical propagating degrees of freedom, which, as compared to the two degrees of freedom of general relativity, makes the dynamics much more intricate. In particular, we discuss the amount of gauge and physical degrees of freedom for different polarities and multipoles. Finally, as an interesting application, we analyze static nonbidiagonal backgrounds and derive the corresponding perturbative equations., Comment: For a better clarity, some notation has been changed. Matches the published version

Unlike general relativity, in bimetric gravity linear gravitational waves do not evolve as free fields. In this theory there are two types of tensor perturbations, whose interactions are inherited from non-trivial couplings between two dynamical metric tensor fields in the Hassan-Rosen action, and are responsible for the phenomenon of bigravity oscillations. In this work, we analyze the dynamics of cosmological tensor modes in bimetric gravity on sub-horizon scales and close to the general relativity limit. In this limit, the system has a characteristic length scale $L$ that is strictly contained within the comoving Hubble radius. Thus, depending on the magnitude of the comoving wavelength $\lambda$ relative to $L$, we identify two regimes of interest where the system can be studied analytically: (i) deep sub-horizon modes with $\lambda\ll L$, whose dynamics can be studied using multiple scale analysis and are characterized by small and slowly evolving super-imposed perturbations; (ii) sub-horizon modes with $\lambda\gg L$, where the dynamics is characterized by fast super-imposed oscillations that can be studied using asymptotic techniques for highly oscillatory problems. Furthermore, our analysis represents a substantial improvement compared to previous analyses based on a generalization of the WKB method, which, as we show, is ill-suited to study the system at hand., Comment: 30 pages, 6 figures

We study the dynamics of the homogeneous and isotropic cosmological background in the recently proposed ``quantum phenomenological gravitational dynamics'', characterised by logarithmic corrections to the Bekenstein entropy. We show that the model admits a family of solutions that are self-accelerating both at early and late times: they approach de Sitter in the future and admit a past attractor corresponding to an inflationary acceleration era. On the other hand, there are no solutions corresponding to a primordial bounce. We also show that asking scalar perturbations to be unaffected by instabilities on observable scales puts stringent constraints on the deviations from general relativity encoded by the model., Comment: 14 pages, 2 figures

We study the accretion of a Schwarzschild black hole due to spherically symmetric perturbations sourced by a minimally coupled massless scalar field. The backreaction of the black hole to low-frequency ingoing scalar waves is computed analytically as a second-order perturbative effect, using matched asymptotic expansions to relate the behaviour of the scalar field in the vicinity of the horizon and at null infinity. As an application of our results, we compute the mass increase due to (i) ingoing wave packets with an arbitrary profile and (ii) incoherent radiation. Our results could serve as a model for the backreaction of environmental scalar fields on black holes., Comment: 10 pages, 3 figures; v2: updated references, matches published version in PRD

Considering a generalization of the Gibbons-Hawking-York covariant boundary action that depends on both the extrinsic and the intrinsic geometry of the boundary, we derive boundary conditions for the cosmological background and tensor perturbations in a closed universe with space-like boundaries. We also give a general method to reconstruct the covariant boundary action starting from a given set of boundary conditions for the cosmological background. These results may be of special relevance in the context of the path-integral formulation of quantum cosmology, where boundary terms contain essential physical information of the system., Comment: 11 pages; v2: references updated; matches version accepted for publication in PRD

We obtain approximate analytical solutions of the Einstein equations close to the trapping horizon for a dynamical spherically symmetric black hole in the presence of a minimally coupled self-interacting scalar field. This is made possible by a new parametrization of the metric, in which the displacement from the horizon as well as its expansion rate feature explicitly. Our results are valid in a neighbourhood of the horizon and hold for any scalar field potential and spacetime asymptotics. An exact equation for the accretion rate is also obtained, which generalizes the standard Bondi formula. We also develop a dynamical system approach to study near-equilibrium black holes; using this formalism, we focus on a simple model to show that the near-equilibrium dynamics is characterised by scaling relations among dynamical variables. Moreover, we show that solutions with purely ingoing energy-momentum flux never reach equilibrium., Comment: 13 pages, 1 figure

In trace-free Einstein gravity, the stress-energy tensor of matter is not necessarily conserved and so the theory offers a natural framework for interacting dark energy models where dark energy has a constant equation of state $w=-1$. We derive the equations of motion for linear cosmological perturbations in interacting dark energy models of this class, focusing on the scalar sector. Then, we consider a specific model where the energy-momentum transfer potential is proportional to the energy density of cold dark matter; this transfer potential has the effect of inducing an effective equation of state $w_{\rm eff}\neq0$ for cold dark matter. We analyze in detail the evolution of perturbations during radiation domination on super-Hubble scales, finding that the well-known large-scale instability that affects a large class of interacting dark energy models is absent in this model. To avoid a gradient instability, energy must flow from dark matter to dark energy. Finally, we show that interacting dark energy models with $w=-1$ are equivalent to a class of generalized dark matter models., Comment: 23 pages + references; accepted for publication in PRD

Starting from a local action for mimetic gravity that includes higher derivatives of a scalar field $\phi$, we derive a gauge-fixed canonical action of the theory in the ADM canonical formalism in the time gauge $\phi=t$. This reduced action reveals (i) a non-vanishing conserved physical Hamiltonian that is a sum of two terms, the expression for the Hamiltonian constraint of general relativity and a function of the expansion scalar, and (ii) a reduced symplectic structure that geometrically provides the Dirac brackets. As applications of our general analysis, we compute the physical Hamiltonians and canonical equations for perturbations around Minkowski spacetime, homogeneous cosmologies, and spherically symmetric spacetimes., Comment: 23 pages

The dynamics of the vacuum Kantowski-Sachs space-time are studied in the so-called limiting curvature mimetic gravity theory. It is shown that in this theory the vacuum Kantowski-Sachs space-time is always singular. While the departures from general relativity due to the limiting curvature mimetic theory do provide an upper bound on the magnitude of the expansion scalar, both its rate of oscillations and the magnitude of the directional Hubble rates increase without bound and cause curvature invariants to diverge. Also, since the radial scale factor does not vanish in finite (past) time, in this particular theory the Kantowski-Sachs space-time cannot be matched to a null black hole event horizon and, therefore, does not correspond to the interior of a static and spherically symmetric black hole., Comment: 24 pages + appendices and references, 10 figures; v2: matches version accepted for publication in JCAP

We derive transition rules for Kasner exponents in bouncing Bianchi I models with generic perfect fluid matter fields for a broad class of modified gravity theories where cosmological singularities are resolved and replaced by a non-singular bounce. This is a generalization of results obtained previously in limiting curvature mimetic gravity and loop quantum cosmology. A geometric interpretation is provided for the transition rule as a linear map in the Kasner plane. We show that the general evolution of anisotropies in a Bianchi I universe -- including during the bounce phase -- is equivalent to the motion of a point particle on a sphere, where the sphere is the one-point compactification of the Kasner plane. In addition, we study the evolution of anisotropies in a large family of bouncing Bianchi I space-times. We also present a novel explicit solution to the Einstein equations for a Bianchi I universe with ekpyrotic matter with a constant equation of state $\omega=3$., Comment: 28 pages, 2 figures; v2: references added; accepted for publication in JCAP

We illustrate a general reconstruction procedure for mimetic gravity. Focusing on a bouncing cosmological background, we derive general properties that must be satisfied by the function $f(\Box\phi)$ implementing the limiting curvature hypothesis. We show how relevant physical information can be extracted from power law expansions of $f$ in different regimes, corresponding e.g. to the very early universe or to late times. Our results are then applied to two specific models reproducing the cosmological background dynamics obtained in group field theory and in loop quantum cosmology, and we discuss the possibility of using this framework as providing an effective field theory description of quantum gravity. We study the evolution of anisotropies near the bounce, and discuss instabilities of scalar perturbations. Furthermore, we discuss two equivalent formulations of mimetic gravity: one in terms of an effective fluid with exotic properties, the other featuring two distinct time-varying gravitational "constants" in the cosmological equations., Comment: Invited article for the special issue "Progress in Group Field Theory and Related Quantum Gravity Formalisms" of the journal "Universe"; 21 pages, 2 figures; v2: matches published version

Nonsingular bouncing cosmologies are realized in limiting curvature mimetic gravity by means of a multi-valued potential $f(\Box\phi)$ depending on the d'Alembertian of a scalar field $\phi$. We determine the functional form of such a potential so as to exactly reproduce the cosmological background dynamics obtained in the group field theory approach to quantum gravity. The original proposal made by Chamseddine and Mukhanov [JCAP 1703, no. 03, 009 (2017)], which was shown to lead to a background dynamics reproducing the effective dynamics of loop quantum cosmology, is here recovered as a particular case for some specific choices of the parameters of our model. We also clarify some issues related to the multi-valuedness of the function $f$, showing in particular that its functional form can be unambiguously reconstructed by imposing appropriate matching conditions at the branching points., Comment: 27 pages, 2 figures; v2:added references, matches published version in PRD

We build a noncommutative extension of Palatini-Holst theory on a twist-deformed spacetime, generalizing a model that has been previously proposed by Aschieri and Castellani. The twist deformation entails an enlargement of the gauge group, and leads to the introduction of new gravitational degrees of freedom. In particular, the tetrad degrees of freedom must be doubled, thus leading to a bitetrad theory of gravity. The model is shown to exhibit new duality symmetries. The introduction of the Holst term leads to a dramatic simplification of the dynamics, which is achieved when the Barbero-Immirzi parameter takes the value $\beta=-i$, corresponding to a self-dual action. We study in detail the commutative limit of the model, focusing in particular on the role of torsion and non-metricity. The effects of spacetime noncommutativity are taken into account perturbatively, and are computed explicitly in a simple example. Connections with bimetric theories and the role of local conformal invariance in the commutative limit are also explored., Comment: 52 pages; v2: added references, corrected minor typos; matches published version

In this thesis, we study the implications of Quantum Gravity models for the dynamics of spacetime and the ensuing departures from classical General Relativity. The main focus is on cosmological applications, particularly the impact of quantum gravitational effects on the dynamics of a homogenous and isotropic cosmological background. Our interest lies in the consequences for the evolution of the early universe and singularity resolution, as well as in the possibility of providing an alternative explanation for dark matter and dark energy in the late universe. The thesis is divided into two main parts, dedicated to alternative (and complementary) ways of tackling the problem of Quantum Gravity. The first part is concerned with cosmological applications of background independent approaches to Quantum Gravity, both in the context of loop quantisation and in quantum geometrodynamics. Particularly relevant in this work is the Group Field Theory approach, which we use to study the effective dynamics of the emergent universe from a full theory of Quantum Gravity (i.e. without symmetry reduction). In the second part, modified gravity theories are introduced as tools to provide an effective description of quantum gravitational effects, e.g. by introducing new degrees of freedom and symmetries. Particularly relevant in this respect is local conformal invariance, which finds a natural realisation in the framework of Weyl geometry. We build a modified theory of gravity based on such symmetry principle, and argue that new fields in the extended gravitational sector may play the role of dark matter. New degrees of freedom are also natural in models with varying fundamental `constants', which we examine critically. Finally, we discuss prospects for future work and point at directions for the derivation of realistic cosmological models from Quantum Gravity candidates., Comment: PhD thesis, King's College London (supervisor: Mairi Sakellariadou), 282 pages, 20 figures; submitted in September 2017

We study the dynamics of perturbations representing deviations from perfect isotropy in the context of the emergent cosmology obtained from the group field theory formalism for quantum gravity. Working in the mean field approximation of the group field theory formulation of the Lorentzian EPRL model, we derive the equations of motion for such perturbations to first order. We then study these equations around a specific simple isotropic background, characterised by the fundamental representation of $\mbox{SU(2)}$, and in the regime of the effective cosmological dynamics corresponding to the bouncing region replacing the classical singularity, well approximated by the free GFT dynamics. In this particular example, we identify a region in the parameter space of the model such that perturbations can be large at the bounce but become negligible away from it, i.e. when the background enters the non-linear regime. We also study the departures from perfect isotropy by introducing specific quantities, such as the surface-area-to-volume ratio and the effective volume per quantum, which make them quantitative., Comment: 45 pages, 4 figures

The aim of these notes is to give an accessible and self-contained introduction to the theory of gravitational waves as the theory of a relativistic symmetric tensor field in a Minkowski background spacetime. This is the approach of a particle physicist: the graviton is identified with a particular irreducible representation of the Poincar\'e group, corresponding to vanishing mass and spin two. It is shown how to construct an action functional giving the linear dynamics of gravitons, and how General Relativity can be obtained from it. The Hamiltonian formulation of the linear theory is examined in detail. We study the emission of gravitational waves and apply the results to the simplest case of a binary Newtonian system., Comment: 47 pages, 3 figures, v2 matches the published version

We introduce an extension of the Standard Model and General Relativity built upon the principle of local conformal invariance, which represents a generalization of a previous work by Bars, Steinhardt and Turok. This is naturally realized by adopting as a geometric framework a particular class of non-Riemannian geometries, first studied by Weyl. The gravitational sector is enriched by a scalar and a vector field. The latter has a geometric origin and represents the novel feature of our approach. We argue that physical scales could emerge from a theory with no dimensionful parameters, as a result of the spontaneous breakdown of conformal and electroweak symmetries. We study the dynamics of matter fields in this modified gravity theory and show that test particles follow geodesics of the Levi-Civita connection, thus resolving an old criticism raised by Einstein against Weyl's original proposal., Comment: 11 pages; v2: matches published version in EPJC; new title, includes new sections on the coupling of matter fields to the extended gravitational sector

We study the cosmological implications of interactions between spacetime quanta in the Group Field Theory (GFT) approach to Quantum Gravity from a phenomenological perspective. Our work represents a first step towards understanding Early Universe Cosmology by studying the dynamics of the emergent continuum spacetime, as obtained from a fundamentally discrete microscopic theory. In particular, we show how GFT interactions lead to a recollapse of the Universe while preserving the bounce replacing the initial singularity, which has already been shown to occur in the free case. It is remarkable that cyclic cosmologies are thus obtained in this framework without any a priori assumption on the geometry of spatial sections of the emergent spacetime. Furthermore, we show how interactions make it possible to have an early epoch of accelerated expansion, which can be made to last for an arbitrarily large number of e-folds, without the need to introduce an ad hoc potential for the scalar field., Comment: 11 pages, 6 figures

We consider implications of the microscopic dynamics of spacetime for the evolution of cosmological models. We argue that quantum geometry effects may lead to stochastic fluctuations of the gravitational constant, which is thus considered as a macroscopic effective dynamical quantity. Consistency with Riemannian geometry entails the presence of a time-dependent dark energy term in the modified field equations, which can be expressed in terms of the dynamical gravitational constant. We suggest that the late-time accelerated expansion of the Universe may be ascribed to quantum fluctuations in the geometry of spacetime rather than the vacuum energy from the matter sector., Comment: 10 pages, 1 figure, v2: added legend in Fig.1 and a reference

We study the expansion of the Universe using an effective Friedmann equation obtained from the dynamics of GFT (Group Field Theory) isotropic condensates. The evolution equations are classical, with quantum correction terms to the Friedmann equation given in the form of effective fluids coupled to the emergent classical background. The occurrence of a bounce, which resolves the initial spacetime singularity, is shown to be a general property of the model. A promising feature of this model is the occurrence of an era of accelerated expansion, without the need to introduce an inflaton field with an appropriately chosen potential. We discuss possible viability issues of this scenario as an alternative to inflation., Comment: 14 pages, 4 figures, v2 revised to match published version

We consider an extension of WDW minisuperpace cosmology with additional interaction terms that preserve the linear structure of the theory. General perturbative methods are developed and applied to known semiclassical solutions for a closed Universe filled with a massless scalar. The exact Feynman propagator of the free theory is derived by means of a conformal transformation in minisuperspace. As an example, a stochastic interaction term is considered and first order perturbative corrections are computed. It is argued that such an interaction can be used to describe the interaction of the cosmological background with the microscopic d.o.f. of the gravitational field. A Helmoltz-like equation is considered for the case of interactions that do not depend on the internal time and the corresponding Green's kernel is obtained exactly.The possibility of linking this approach to fundamental theories of Quantum Gravity is investigated., Comment: 18 pages, 5 figures

Recent work in the literature has argued that the joint effect of spacetime curvature and the Gribov ambiguity may introduce further modifications to the Green functions in the infrared. This paper focuses on a simple criterion for studying the effect of spacetime curvature on the size of the Gribov region, improving the accuracy of the previous analysis. It is shown that, depending on the sign of the scalar and Riemann curvature, the Gribov horizon moves inward or, instead, outward with respect to the case of flat spacetime. This is made clear by two novel inequalities here derived for the first time., Comment: 11 pages, Revtex4. Section 5 has been added. References from 10 to 17 have been added. arXiv admin note: text overlap with arXiv:1308.5344

The quantization of Yang-Mills theories relies on the gauge-fixing procedure. However, in the non-Abelian case this procedure leads to the well known Gribov ambiguity. In order to solve the ambiguity a modification of the functional integral formula must be introduced. As a consequence of this, the Green functions get deep modifications in the infrared. We consider in particular the SU (N) case and show that in the pure gauge case the ghost propagator is enhanced, while the gluon propagator is suppressed in this limit, therefore the study of the Gribov ambiguity may shed some light on the mass gap problem and on colour confinement. We discuss some recent developments on the subject in the case of a curved background. We argue that the concurrent presence of a spacetime curvature and the Gribov ambiguity may introduce further modifications to the Green functions in the infrared., Comment: 87 pages, 8 figures