We discuss the presence of ghostly instabilities for metric-affine theories constructed with higher order curvature terms. We mainly focus on theories containing only the Ricci tensor and show the crucial role played by the projective symmetry. The pathological modes arise from the absence of a pure kinetic term for the projective mode and the non-minimal coupling of a 2-form field contained in the connection, and which can be related to the antisymmetric part of the metric in non-symmetric gravity theories. The couplings to matter are considered at length and cannot be used to render the theories stable. We discuss different procedures to avoid the ghosts by adding additional constraints. We finally argue how these pathologies are expected to be present in general metric-affine theories unless much care is taken in their construction.
We investigate instabilities and their regularization in theories of gravitation. Instabilities can be beneficial since their growth often leads to prominent observable signatures which makes them especially relevant to relatively low signal-to-noise ratio measurements such as gravitational wave detections. An indefinitely growing instability usually renders a theory unphysical, hence a desirable instability should also come with underlying physical machinery that stops the growth at finite values, i.e. regularization mechanisms. The prototypical gravity theory that presents such an instabilit…
We extend the scope of the Raychaudhuri-Komar singularity theorem of General Relativity to affine theories of gravity with and without torsion. We first generalize the existing focusing theorems using time-like and null congruences of curves which are hypersurface orthogonal, showing how the presence of torsion affects the formation of focal points in Lorentzian manifolds. Considering the energy conservation on a given affine gravity theory, we prove new singularity theorems for accelerated curves in the cases of Lorentzian manifolds containing perfect fluids or scalar field matter sources.
In this paper we extend the projective symmetry of the full metric-affine Einstein-Hilbert theory to a new symmetry transformation in the space of affine connections called the amplified symmetry. We prove that the Lagrangian of the Standard Model of particle physics is invariant under this new symmetry. We also show that the gravitational Lagrangian can be modified so that the amplified symmetry extends to the gravitational sector and hence to the whole action. The new theory so constructed is shown to be dynamically equivalent to Einstein-Cartan's though genuinely metric-affine.
We study f(R,T) theories of gravity, where T is the trace of the energy-momentum tensor T_{μν}, with independent metric and affine connection (metric-affine theories). We find that the resulting field equations share a close resemblance with their metric-affine f(R) relatives once an effective energy-momentum tensor is introduced. As a result, the metric field equations are second-order and no new propagating degrees of freedom arise as compared to GR, which contrasts with the metric formulation of these theories, where a dynamical scalar degree of freedom is present. Analogously to its metric…
We explore ways to obtain the very existence of a space-time metric from an action principle that does not refer to it a priori. Although there are reasons to believe that only a non-local theory can viably achieve this goal, we investigate here local theories that start with Schroedinger's purely affine theory [21], where he gave reasons to set the metric proportional to the Ricci curvature aposteriori. When we leave the context of unified field theory, and we couple the non-gravitational matter using some weak equivalence principle, we can show that the propagation of shock waves does not de…
We study the Hamiltonian formalism of the non-minimally coupled Weyl connection gravity (NMCWCG) in order to check whether Ostrogradsky instabilities are present. The Hamiltonian of the NMCWCG theories is obtained by foliating space-time into a real line (representing time) and \mbox{3-dimensional} space-like hypersurfaces, and by considering the spatial metric and the extrinsic curvature of the hypersurfaces as the canonical coordinates of the theory. Given the fact that the theory we study contains an additional dynamical vector field compared to the usual NMC models, which do not have Ostro…
This work provides a short but comprehensible overview of some relevant aspects of metric-affine theories of gravity in relation to the physics and astrophysics of compact objects. We shall highlight the pertinence of this approach to supersede General Relativity on its strong-field regime, as well as its advantages and some of its difficulties. Moreover, we shall reflect on the present and future opportunities to testing its predictions with relativistic and non-relativistic stars, black holes, and other exotic horizonless compact objects.
We undertake the construction of quadratic parity-violating terms involving the curvature in the four-dimensional metric-affine gravity. We demonstrate that there are only 12 linearly independent scalars, plus an additional one that can be removed by using the Pontryagin invariant. Several convenient bases for this sector are provided in both components and differential form notation. We also particularize our general findings to some constrained geometries like Weyl-Cartan and metric-compatible connections.
The recent direct detection of gravitational waves has highlighted the huge importance of the tensorial modes in any extended gravitational theory. One of the most appealing approaches to extend gravity beyond general relativity is the Eddington-inspired-Born-Infeld gravity which is formulated within the Palatini approach. This theory can avoid the Big Bang singularity in the physical metric although a Big Bang intrinsic to the affine connection is still there, which in addition couples to the tensorial sector and might jeopardize the viability of the model. In this paper, we suggest that a qu…
How to include spacetime translations in fibre bundle gauge theories has been a subject of controversy, because spacetime symmetries are not internal symmetries of the bundle structure group. The standard method for including affine symmetry in differential geometry is to define a Cartan connection on an affine bundle over spacetime. This is equivalent to (1) defining an affine connection on the affine bundle, (2) defining a zero section on the associated affine vector bundle, and (3) using the affine connection and the zero section to define an "associated solder form," whose lift to a tensor…
Modified theories of gravity usually present new degrees of freedom, as well as higher order derivatives, wrong signs in certain terms and complicated couplings already present in the Lagrangian from the beginning or originated by the field redefinitions needed to reach an Einstein frame. As a consequence, they are very prone to present dynamical instabilities that could spoil any attempt to construct viable models within these frameworks. In these three lectures we introduce the most common types of instabilities that appear in field theory as well as some techniques to detect them, and suppl…
Among the general class of metric-affine theories of gravity, there is a special class conformed by those endowed with a projective symmetry. Perhaps the simplest manner to realise this symmetry is by constructing the action in terms of the symmetric part of the Ricci tensor. In these theories, the connection can be solved algebraically in terms of a metric that relates to the spacetime metric by means of the so-called deformation matrix that is given in terms of the matter fields. In most phenomenological applications, this deformation matrix is assumed to inherit the symmetries of the matter…
We study the superradiant instability in scalar-tensor theories of gravitation, where matter outside a black hole provides an effective mass to the scalar degree of freedom of the gravitational sector. We discuss this effect for arbitrarily spinning black holes and for realistic models of truncated thin and thick accretion disks (where the perturbation equations are nonseparable), paying particular attention to the role of hot coronal flows in the vicinity of the black hole. The system qualitatively resembles the phenomenology of plasma-driven superradiant instabilities in General Relativity. …
We propose a novel class of degenerate higher-order scalar-tensor theories as an extension of mimetic gravity. By performing a noninvertible conformal transformation on "seed" scalar-tensor theories which may be nondegenerate, we can generate a large class of theories with at most three physical degrees of freedom. We identify a general seed theory for which this is possible. Cosmological perturbations in these extended mimetic theories are also studied. It is shown that either of tensor or scalar perturbations is plagued with gradient instabilities, except for a special case where the scalar …
In this paper we review the Myrzakulov Gravity models (MG-N, with $\mathrm{N = I, II, \ldots, VIII}$) and derive their respective metric-affine generalizations (MAMG-N), discussing also their particular sub-cases. The field equations of the theories are obtained by regarding the metric tensor and the general affine connection as independent variables. We then focus on the case in which the function characterizing the aforementioned metric-affine models is linear and consider a Friedmann-Lemaître-Robertson-Walker background to study cosmological aspects and applications.
It is well known that the teleparallel equivalent of general relativity yields the same vacuum solutions as general relativity does, which ensures that this particular teleparallel model is in good agreement with experiments. A less known result concerns the existence of a wider class of teleparallel models which also admits these solutions when the spacetime is diagonalizable by means of a coordinate change. However, it is stated in Ref. [Phys. Rev. D 67, 044016 (2003).] that the teleparallel equivalent of general relativity is the only teleparallel model which admits black holes. To show tha…
The intriguing choice to treat alternative theories of gravity by means of the Palatini approach, namely elevating the affine connection to the role of independent variable, contains the seed of some interesting (usually under-explored) generalizations of General Relativity, the metric-affine theories of gravity. The peculiar aspect of these theories is to provide a natural way for matter fields to be coupled to the independent connection through the covariant derivative built from the connection itself. Adopting a procedure borrowed from the effective field theory prescriptions, we study the …
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 …
In full Horndeski theories, we show that the static and spherically symmetric black hole (BH) solutions with a static scalar field~$ϕ$ whose kinetic term~$X$ is nonvanishing on the BH horizon are generically prone to ghost/Laplacian instabilities. We then search for asymptotically Minkowski hairy BH solutions with a vanishing $X$ on the horizon free from ghost/Laplacian instabilities. We show that models with regular coupling functions of $ϕ$ and $X$ result in no-hair Schwarzschild BHs in general. On the other hand, the presence of a coupling between the scalar field and the Gauss-Bonnet (GB) …
We reveal the existence of a certain hidden symmetry in general ghost-free scalar-tensor theories which can only be seen when generalizing the geometry of the spacetime from Riemannian. For this purpose, we study scalar-tensor theories in the metric-affine (Palatini) formalism of gravity, which we call scalar-metric-affine theories for short, where the metric and the connection are independent. We show that the projective symmetry, a local symmetry under a shift of the connection, can provide a ghost-free structure of scalar-metric-affine theories. The ghostly sector of the second-order deriva…
It is expected that the Gregory-Laflamme (GL) instability in the black string in gravity is related to the Rayleigh-Plateau instability in fluid mechanics. Especially, the orders of the phase transitions associated with these instabilities depend on the number of the transverse space dimensions, and they are of first and second order below and above the critical dimension. Through the gauge-gravity correspondence, the GL instability is conjectured to be thermodynamically related to the Hagedorn instability in large-N gauge theories, and it leads to a prediction that the order of the confinemen…
In a geometrical approach to gravity the metric and the (gravitational) connection can be independent and one deals with metric-affine theories. We construct the most general action of metric-affine effective field theories, including a generic matter sector, where the connection does not carry additional dynamical fields. Among other things, this helps in identifying the complement set of effective field theories where there are other dynamical fields, which can have an interesting phenomenology. Within the latter set, we study in detail a vast class where the Holst invariant (the contraction…
The review is devoted to consideration of possible observational consequences of modified gravity theories, suggested for explanation of the contemporary accelerated expansion of the universe. The major attention is paid to F(R)-models. It is shown that in systems with rising energy density high frequency and large amplitude oscillations of the curvature scalar, R(t), are induced. These oscillations lead to the production of elementary particles, which may be observed in the spectra of energetic cosmic rays. In the background of such oscillating solutions gravitation repulsion between finite-s…
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 …
We give a geometrical description of gravitational theories from the viewpoint of symmetries and affine structure. We show how gravity, considered as a gauge theory, can be consistently achieved by the nonlinear realization of the conformal-affine group in an indirect manner: due the partial isomorphism between $CA\left( 3,1\right) $ and the centrally extended $Sp\left( 8\right) $, we perform a nonlinear realization of the centrally extended (CE)$Sp\left( 8\right) $ in its semi-simple version. In particular, starting from the bundle structure of gravity, we derive the conformal-affine Lie alge…
In metric-affine theories of gravity such as the C-theories, the spacetime connection is associated to a metric that is nontrivially related to the physical metric. In this article, such theories are rewritten in terms of a single metric and it is shown that they can be recast as effectively nonlocal gravity. With some assumptions, known ghost-free theories with non-singular and cosmologically interesting properties may be recovered. Relations between different formulations are analysed at both perturbative and nonperturbative levels taking carefully into account subtleties with boundary condi…
In this work we study the stability of the four vector irreducible pieces of the torsion and the nonmetricity tensors in the general quadratic metric-affine Lagrangian in 4 dimensions. The goal will be to elucidate under which conditions the spin-1 modes associated to such vectors can propagate in a safe way, together with the graviton. This highly constrains the theory reducing the parameter space of the quadratic curvature part from 16 to 5 parameters. We also study the sub-case of Weyl-Cartan gravity, proving that the stability of the vector sector is only compatible with an Einstein-Proca …
We study scalar-tensor theories respecting the projective invariance in the metric-affine formalism. The metric-affine formalism is a formulation of gravitational theories such that the metric and the connection are independent variables in the first place. In this formalism, the Einstein-Hilbert action has an additional invariance, called the projective invariance, under a shift of the connection. Respecting this invariance for the construction of the scalar-tensor theories, we find that the Galileon terms in curved spacetime are uniquely specified at least up to quartic order which does not …
Universitá di Napoli ”Federico II”（那不勒斯费德里科二世大学）；Scuola Superiore Meridionale（南方高等学院）；Istituto Nazionale di Fisica Nucleare – Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）
In this PhD thesis we deal with several theoretical and phenomenological apsects of metric-affine theories of gravity. Concretely, we first give a broad introduction to the necessary tools to understand the framework and elaborate on some subtleties of the minimal coupling prescription between geometry and matter in presence of torsion and nonmetricity. Then we dedicate the central part of the thesis to study the structure of Ricci Based gravity (RBG) theories, which will be of later use to understand generic properties of metric-affine theories. We begin by analysing the structure of the RBG …
In the first part, we discuss the interplay between local scale invariance and metric-affine degrees of freedom from few distinct points of view. We argue, rather generally, that the gauging of Weyl symmetry is a natural byproduct of requiring that scale invariance is a symmetry of a gravitational theory that is based on a metric and on an independent affine structure degrees of freedom. In the second part, we compute the Nöther identities associated with all the gauge symmetries, including Weyl, Lorentz and diffeomorphisms invariances, for general actions with matter degrees of freedom, explo…
This thesis covers several developments performed in metric-affine gravity. This alternative framework extends General Relativity by considering a more general connection than the one induced by the metric (i.e., arbitrary torsion and nonmetricity participate in the dynamics). We start by revising some mathematical aspects of the metric-affine framework, the way Lovelock and other invariants are extended to it and the construction of a gauge formalism. Then we focus on metric-affine pp-wave geometries and explore solutions of this type for the quadratic metric-affine Lagrangian (with even-pari…
The behavior of fundamental fields in strong gravity or nontrivial environments is important for our understanding of nature. This problem has interesting applications in the context of dark matter, of dark energy physics or of quantum field theory. The dynamics of fundamental fields has been studied mainly in static or stationary backgrounds, whereas most of our Universe is dynamic. In this paper we investigate "blueshift" and parametric instabilities of scalar fields in dynamical backgrounds, which can be triggered (for instance) by oscillating stars in scalar-tensor theories of gravity. We …
We revisit the gauge symmetry related to integrable projective transformations in metric-affine formalism, identifying the gauge field of the Weyl (conformal) symmetry as a dynamical component of the affine connection. In particular, we show how to include the local scaling symmetry as a gauge symmetry of a large class of geometric gravity theories, introducing a compensator dilaton field that naturally gives rise to a Stückelberg sector where a spontaneous breaking mechanism of the conformal symmetry is at work to generate a mass scale for the gauge field. For Ricci-based gravities that inclu…
We study a parity violating Metric-Affine gravitational theory given by the Einstein-Hilbert action plus the so-called Holst term in vacuum. We find out that for a certain value of the Barbero-Immirzi parameter the total action possesses a remarkable invariance under particular transformations of the affine connection. We prove that in all cases, with appropriate gauge choices, the connection reduces to the Levi-Civita one and that the theory turns out to be equivalent to general relativity in vacuum. Subsequently, we generalize our discussion and analyze the case of Metric-Affine $f(R)$ gravi…
Teleparallel geometry offers a platform on which to build up theories of gravity where torsion rather than curvature mediates gravitational interaction. The teleparallel analogue of Horndeski gravity is an approach to teleparallel geometry where scalar-tensor theories are considered in this torsional framework. Being teleparallel gravity of lower order in dynamics, this turns out to be more general than metric Horndeski gravity. In other words, the class of teleparallel Horndeski gravity models is much broader than the standard metric one. In this work, we explore constraints on this wide rang…
Perturbations and eikonal instabilities of black holes and branes in the Einstein-Gauss-Bonnet theory and its Lovelock generalization were considered in the literature for several particular cases, where the asymptotic conditions (flat, dS, AdS), the number of spacetime dimensions $D$, non-vanishing coupling constants ($α_1$, $α_2$, $α_3$ etc.) and other parameters have been chosen in a specific way. Here we give a comprehensive analysis of the eikonal instabilities of black holes and branes for the \emph{most general} Lovelock theory, not limited by any of the above cases. Although the part o…
Minisuperpace Quantum Cosmology is an approach by which it is possible to infer initial conditions for dynamical systems which can suitably represent observable and non-observable universes. Here we discuss theories of gravity which, from various points of view, extend Einstein's General Relativity. Specifically, the Hamiltonian formalism for $f(R)$, $f(T)$ and $f(\mathcal{G})$ gravity, with $R$, $T$, and $\mathcal{G}$ being the curvature, torsion and Gauss--Bonnet scalars, respectively, is developed starting from the Arnowitt-Deser-Misner approach. The Minisuperspace Quantum Cosmology is deri…
A number of stability criteria exist for dark energy theories, associated with requiring the absence of ghost, gradient and tachyonic instabilities. Tachyonic instabilities are the least well explored of these in the dark energy context and we here discuss and derive criteria for their presence and size in detail. Our findings suggest that, while the absence of ghost and gradient instabilities is indeed essential for physically viable models and so priors associated with the absence of such instabilities significantly increase the efficiency of parameter estimations without introducing unphysi…
We briefly describe the simplest class of affine theories of gravity in multidimensional space-times with symmetric connections and their reductions to two-dimensional dilaton - vecton gravity field theories (DVG). The distinctive feature of these theories is the presence of an absolutely neutral massive (or tachyonic) vector field (vecton) with essentially nonlinear coupling to the dilaton gravity (DG). We show that in DVG the vecton field can be consistently replaced by an effectively massive scalar field (scalaron) with an unusual coupling to dilaton gravity. With this vecton - scalaron dua…
Theories with higher order time derivatives generically suffer from ghost-like instabilities, known as Ostrogradski instabilities. This fate can be avoided by considering "degenerate" Lagrangians, whose kinetic matrix cannot be inverted, thus leading to constraints between canonical variables and a reduced number of physical degrees of freedom. In this work, we derive in a systematic way the degeneracy conditions for scalar-tensor theories that depend quadratically on second order derivatives of a scalar field. We thus obtain a classification of all degenerate theories within this class of sca…
Some classical aspects of Metric-Affine Gravity are reviewed in the context of the $F^{(n)}(R)$ type models (polynomials of degree $n$ in the Riemann tensor) and the topologically massive gravity. At the non-perturbative level, we explore the consistency of the field equations when the $F^{(n)}(R)$ models are reduced to a Riemann-Christoffel (RCh) space-time, either via a Riemann-Cartan (RC) space or via an Einstein-Weyl (EW) space. It is well known for the case $F^{(1)}(R)=R$ that any path or reduction "classes" via RC or EW, leads to the same field equations with the exception of the $F^{(n)…
We study linear perturbations about static and spherically symmetric black holes with a time-independent background scalar field in shift-symmetric Horndeski theories, whose Lagrangian is characterized by coupling functions depending only on the kinetic term of the scalar field $X$. We clarify conditions for the absence of ghosts and Laplacian instabilities along the radial and angular directions in both odd- and even-parity perturbations. For reflection-symmetric theories described by a k-essence Lagrangian and a nonminimal derivative coupling with the Ricci scalar, we show that black holes e…
Nowadays it is widely accepted that the evolution of the universe was driven by some scalar degrees of freedom both on its early stage and at present. The corresponding cosmological models often involve some scalar fields introduced ad hoc. In this paper we cultivate a different approach, which is based on a derivation of new scalar degrees of freedom from fundamental modifications of Einstein's gravity. In elaboration of our previous work, we here investigate properties of the dilaton-scalar gravity obtained by dimensional reductions of a recently proposed affine generalized gravity theory. W…
Metric-affine theories of gravity provide an interesting alternative to General Relativity: in such an approach, the metric and the affine (not necessarily symmetric) connection are independent quantities. Furthermore, the action should include covariant derivatives of the matter fields, with the covariant derivative naturally defined using the independent connection. As a result, in metric-affine theories a direct coupling involving matter and connection is also present. The role and the dynamics of the connection in such theories is explored. We employ power counting in order to construct th…
