A class of scalar-tensor theories (STT) including a non-metricity that unifies metric, Palatini and hybrid metric-Palatini gravitational actions with non-minimal interaction is proposed and investigated from the point of view of their consistency with generalized conformal transformations. It is shown that every such theory can be represented on-shell by a purely metric STT possessing the same solutions for a metric and a scalar field. A set of generalized invariants is also proposed. This extends the formalism previously introduced in \cite{kozak2019}. We then apply the formalism to Starobinsky model, write down the Friedmann equations for three possible cases: metric, Palatini and hybrid metric-Palatini, and compare some inflationary observables.
We consider the internal structure and the physical properties of specific classes of neutron, quark and Bose-Einstein Condensate stars in the hybrid metric-Palatini gravity theory, which is a combination of the metric and Palatini $f(R)$ formalisms. The theory is very successful in accounting for the observed phenomenology, since it unifies local constraints at the Solar System level and the late-time cosmic acceleration, even if the scalar field is very light. We derive the equilibrium equations for a spherically symmetric configuration (mass continuity and Tolman-Oppenheimer-Volkoff) in the…
We investigate the thick brane model in Palatini $f(\mathcal{R})$ gravity. The brane is generated by a real scalar field with a scalar potential. We solve the system analytically and obtain a series of thick brane solutions for the $f(\mathcal{R})=\mathcal{R}+α\mathcal{R}^2$-brane model. It is shown that tensor perturbations of the metric are stable for $df({\mathcal{R}})/d{\mathcal{R}}>0$. For nonconstant curvature solutions, the graviton zero mode can be localized on the brane, which indicates that the four-dimensional gravity can be recovered on the brane. Mass spectrum of graviton KK modes…
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 investigate static spherically symmetric solutions in the Palatini kinetically coupled scalar-tensor theory, which reduces to gravity minimally coupled to a scalar field in Einstein frame. Using the fact that the Jordan and Einstein frame are related by a reversible disformal transformation, which can be solved in closed form, we derive the general solution in the Jordan frame and show that it does not contain black holes. There is a wormhole branch and a naked singularity branch between which lies a non-singular asymptotically flat solution with kernel $M_{1,1}\times S^2$. This theory stro…
It is known that the metric and Palatini formalisms of gravity theories have their own interesting features but also suffer from some different drawbacks. Recently, a novel gravity theory called hybrid metric-Palatini gravity was put forward to cure or improve their individual deficiencies. The action of this gravity theory is a hybrid combination of the usual Einstein-Hilbert action and a $f(\mathcal{R})$ term constructed by the Palatini formalism. Interestingly, it seems that the existence of a light and long-range scalar field in this gravity may modify the cosmological and galactic dynamic…
We introduce a new approach to modified gravity which generalizes the recently proposed hybrid metric-Palatini gravity. The gravitational action is taken to depend on a general function of both the metric and Palatini curvature scalars. The dynamical equivalence with a non-minimally coupled bi-scalar field gravitational theory is proved. The evolution of cosmological solutions is studied using dynamical systems techniques.
Using a dynamical system approach we study the cosmological phase space of the generalized hybrid metric-Palatini gravity theory, characterized by the function $f\left(R,\mathcal R\right)$, where $R$ is the metric scalar curvature and $\mathcal R$ the Palatini scalar curvature of the spacetime. We formulate the propagation equations of the suitable dimensionless variables that describe FLRW universes as an autonomous system. The fixed points are obtained for four different forms of the function $f\left(R,\mathcal R\right)$, and the behavior of the cosmic scale factor $a(t)$ is computed. We sho…
In this paper, the hybrid metric-Palatini gravity is an approach to modified gravity in which is added to the usual Einstein-Hilbert action a supplementary term containing a Palatini-type correction of the form $f({\cal R},T)$. Here, ${\cal R}$ is the Palatini curvature scalar, which is constructed from an independent connection and $T$ is the trace of the energy-momentum tensor. This theory describes a non-minimal coupling between matter and geometry. The modified Einstein field equations in this hybrid metric-Palatini approach are obtained. Then, it is investigated whether this modified theo…
The question of the correspondence between the number of degrees of freedom and the number of polarization states in hybrid metric-Palatini f(R)-gravity is considered. It is shown that the scalar transverse breathing and longitudinal modes are a mixture of one polarization state. The speed of gravitational waves propagation in hybrid f(R)-gravity is calculated.
We construct exact solutions representing a Friedmann-Lemaître-Robsertson-Walker (FLRW) universe in a generalized hybrid metric-Palatini theory. By writing the gravitational action in a scalar-tensor representation, the new solutions are obtained by either making an ansatz on the scale factor or on the effective potential. Among other relevant results, we show that it is possible to obtain exponentially expanding solutions for flat universes even when the cosmology is not purely vacuum. We then derive the classes of actions for the original theory which generate these solutions.
We study a general class of gravitational theories formulated in the Palatini approach and derive the equations governing the evolution of tensor perturbations. In the absence of torsion, the connection can be solved as the Christoffel symbols of an auxiliary metric which is non-trivially related to the space-time metric. We then consider background solutions corresponding to a perfect fluid and show that the tensor perturbations equations (including anisotropic stresses) for the auxiliary metric around such a background take an Einstein-like form. This facilitates the study in a homogeneous a…
The well-formulation and the well-posedness of the Cauchy problem is discussed for {\it hybrid metric-Palatini gravity}, a recently proposed modified gravitational theory consisting of adding to the Einstein-Hilbert Lagrangian an $f(R)$ term constructed {\it à la} Palatini. The theory can be recast as a scalar-tensor one predicting the existence of a light long-range scalar field that evades the local Solar System tests and is able to modify galactic and cosmological dynamics, leading to the late-time cosmic acceleration. In this work, adopting generalized harmonic coordinates, we show that th…
The hybrid metric-Palatini theory of gravity (HMPG), proposed in 2012 by T. Harko et al., is known to successfully describe both local (solar-system) and cosmological observations. We discuss static, spherically symmetric vacuum solutions of HMPG with the aid of its scalar-tensor representation. This scalar-tensor theory coincides with general relativity with a conformally coupled scalar field (which can be canonical or phantom), therefore the known solutions of this theory are re-interpreted in terms of HMPG. In particular, in the case of zero scalar field potential $V (ϕ)$, such that both Ri…
We developed the parameterized post-Keplerian formalism for hybrid metric-Palatini $f(R)$-gravity. We obtained analytical expressions in the generel eccentric case for four PPK parameters: $\dotω$, $\dot P_{\rm b}$, $r$ and $s$. Using observational data of PSR J0737-3039 and PSR J1903+0327 we imposed restrictions on the parameters of hybrid f(R)-gravity and showed that this theory is not ruled out by the observations in strong field regime. In addition we obtained predictions for masses of systems components and found that considered astrophysical objects will be heavier than in GR.
We disclose remarkable features of the scalar-tensor theory with the derivative coupling of the scalar field to the curvature in the Palatini formalism. Using the disformal transformations, we show that this theory is free from Otrogradski ghosts. For a special relation between two coupling constants, it is disformally dual to the Einstein gravity minimally coupled to the scalar, which opens the way to constructing several exact solutions. The disformal transformation degenerates at the boundary of the physical region, near which the properties of desingularization are revealed, illustrated by…
Hybrid metric-Palatini gravity is a recent and novel approach to modified theories of gravity, which consists of adding to the metric Einstein-Hilbert Lagrangian an f(R) term constructed a la Palatini. It was shown that the theory passes local tests even if the scalar field is very light, and thus implies the existence of a long-range scalar field, which is able to modify the dynamics in galactic and cosmological scales, but leaves the Solar System unaffected. In this work, motivated by the possibility that the Universe may have started out in an asymptotically Einstein static state in the inf…
We consider vacuum static spherically symmetric solutions in the hybrid metric-Palatini gravity theory, which is a combination of the metric and Palatini $f(R)$ formalisms unifying local constraints at the Solar System level and the late-time cosmic acceleration. We adopt the scalar-tensor representation of the hybrid metric-Palatini theory, in which the scalar-tensor definition of the potential can be represented as a Clairaut differential equation. Due to their mathematical complexity, it is difficult to find exact solutions of the vacuum field equations, and therefore we adopt a numerical a…
We examine the generation of primordial perturbations during an inflationary epoch in generalised theories of gravity when the equations of motion are derived using the Palatini variational principle. Both f(R) and Scalar-Tensor theories are considered and we compare our results with those obtained under the conventional metric formalism. Non-linear generalisations of the action lead to different theories under the two variational choices and we obtain distinct results for scalar and tensor spectral indices and their ratio. We find the following general result; inflation driven solely by f(R) …
Recently, the phenomenology of f(R) gravity has been scrutinized motivated by the possibility to account for the self-accelerated cosmic expansion without invoking dark energy sources. Besides, this kind of modified gravity is capable of addressing the dynamics of several self-gravitating systems alternatively to the presence of dark matter. It has been established that both metric and Palatini versions of these theories have interesting features but also manifest severe and different downsides. A hybrid combination of theories, containing elements from both these two formalisms, turns out to …
The so called $f(X)$ hybrid metric-Palatini gravity presents a unique viable generalisation of the $f(R)$ theories within the metric-affine formalism. Here the cosmology of the $f(X)$ theories is studied using the dynamical system approach. The method consists of formulating the propagation equation in terms of suitable (expansion-normalised) variables as an autonomous system. The fixed points of the system then represent exact cosmological solutions described by power-law or de Sitter expansion. The formalism is applied to two classes of $f(X)$ models, revealing both standard cosmological fix…
The main objective of this thesis is to discuss scalar-tensor theories in the Palatini approach. Both scalar-tensor theories and Palatini formalism are means of alternating classical theory of gravity, general relativity, in order to account for phenomena being seemingly unexplainable on the ground of the Einstein theory or to serve as toy models used to test limitations of the theory in question. In the literature, both Palatini approach and scalar-tensor theories have been widely discussed, but there are very few - if none - authors writing about a merge of these two ideas. The present paper…
Generally, the dynamics of test particles around galaxies, as well as the corresponding mass deficit, is explained by postulating the existence of a hypothetical dark matter. In fact, the behavior of the rotation curves shows the existence of a constant velocity region, near the baryonic matter distribution, followed by a quick decay at large distances. In this work, we consider the possibility that the behavior of the rotational velocities of test particles gravitating around galaxies can be explained within the framework of the recently proposed hybrid metric-Palatini gravitational theory. T…
The generalized hybrid metric-Palatini theory of gravity admits a scalar-tensor representation in terms of two interacting scalar fields. We show that, upon an appropriate choice of the interaction potential, one of the scalar fields behaves like dark energy, inducing a late-time accelerated expansion of the universe, while the other scalar field behaves like pressureless dark matter that, together with ordinary baryonic matter, dominates the intermediate phases of cosmic evolution. This unified description of dark energy and dark matter gives rise to viable cosmological solutions, which repro…
We estimate the parameters of Hybrid Palatini gravity model with the Schwarzschild precession of S-stars, specifically of S2, S38 and S55 stars. We also take into account case of bulk mass distribution near Galactic Center. We assume that the Schwarzschild orbital precession of mentioned S-stars is the same like in General Relativity (GR) in all studied cases. In 2020 the GRAVITY Collaboration detected the orbital precession of the S2 star around the supermassive black hole (SMBH) at the Galactic Center and showed that it is close to the GR prediction. The astronomical data analysis of S38 and…
Recently, a modified theory of gravity was presented, which consists of the superposition of the metric Einstein-Hilbert Lagrangian with an $f(\cal R)$ term constructed à la Palatini. The theory possesses extremely interesting features such as predicting the existence of a long-range scalar field, that explains the late-time cosmic acceleration and passes the local tests, even in the presence of a light scalar field. In this brief report, we consider the possibility that wormholes are supported by this hybrid metric-Palatini gravitational theory. We present here the general conditions for worm…
With a scalar field non-minimally coupled to curvature, the underlying geometry and variational principle of gravity - metric or Palatini - becomes important and makes a difference, as the field dynamics and observational predictions generally depend on this choice. In the present paper we describe a classification principle which encompasses both metric and Palatini models of inflation, employing the fact that inflationary observables can be neatly expressed in terms of certain quantities which remain invariant under conformal transformations and scalar field redefinitions. This allows us to …
We investigate the existence of Liouville integrable cosmological models in hybrid metric-Palatini theory. Specifically we use the symmetry conditions for the existence of quadratic in the momentum conservation laws for the field equations as constraint conditions for the determination of the unknown functional form of the theory. The exact and analytic solutions of the integrable systems which found in this study are presented in terms of quadratics and Laurent expansions.
In this work we discuss the exact solution to the algebraic equation associated to the Ricci tensor in the quadratic $f(R,Q)$ extension of Palatini gravity. We show that an exact solution always exists, and in the general case it can be found by a simple matrix diagonalization. Furthermore, the general implications of the solution are analysed in detail, including the generation of an effective cosmological constant, and the recovery of the $f(R)$ and $f(Q)$ theories as particular cases in their corresponding limit. In addition, it is proposed a power series expansion of the solution which is …
In this work, we analyse the evolution of time-dependent traversable wormhole geometries in a Friedmann-Lemaître-Robertson-Walker background in the context of the scalar-tensor representation of hybrid metric-Palatini gravity. We deduce the energy-momentum profile of the matter threading the wormhole spacetime in terms of the background quantities, the scalar field, the scale factor and the shape function, and find specific wormhole solutions by considering a barotropic equation of state for the background matter. We find that particular cases satisfy the null and weak energy conditions for al…
In this work, we study 5-dimensional braneworld scenarios in the scalar-tensor representation of the generalized hybrid metric-Palatini gravitational theory. We start by considering a model for a brane supported purely by the gravitational scalar fields of the theory and then consider other distinct cases where the models are also supported by an additional matter scalar field. We investigate the stability of the gravity sector and show that the models are all robust against small fluctuations of the metric. In particular, in the presence of the additional scalar field, we find that the profil…
Using the latest most accurate values of post-Newtonian parameters $γ$ and $β$ obtained by MESSENGER we impose restrictions on the recently proposed hybrid f(R)-gravity model in its scalar-tensor representation. We show that the presence of a light scalar field in this theory does not contradict the experimental data based not only on the $ γ$ parameter (as was shown earlier), but also on all other PPN parameters. The application of parameterized post-Newtonian formalism to gravitational theories with massive fields is also discussed.
A new systematic approach extending the notion of frames to the Palatini scalar-tensor theories of gravity in various dimensions n>2 is proposed. We impose frame transformation induced by the group action which includes almost-geodesic and conformal transformations. We characterize theories invariant with respect to these transformations dividing them up into solution-equivalent subclasses (group orbits). To this end, invariant characteristics have been introduced. Unlike in the metric case, it turns out that the dimension four admitting the largest transformation group is rather special for s…
In this work we made use of a general static cillindrically symmetric metric to find $U(1)$ local cosmic string solutions in the context of the hybrid metric-Palatini theory of gravity in it's scalar-tensor representation. After finding the dynamical equations for this particular case, we imposed boost invariance along $t$ and $z$ directions, which simplified the equations of motions, leaving only one single metric tensor component, $W^2(r)$. For an arbitrary potential $V(ϕ)$, the solutions obtained can be put in a closed parametric form, with $ϕ$ taken as a parameter. Several particular cases…
In this paper, we consider the recently proposed hybrid metric-Palatini gravitational theory, which consists of adding to the Einstein-Hilbert Lagrangian an $f(\mathcal{R})$ term constructed à la Palatini. Using the respective dynamically equivalent scalar-tensor representation, we explore the cosmological evolution of a specific model, given by $f(\mathcal{R}) \propto \mathcal{R}^2$, and obtain constraints on the free parameters by using different sources of cosmological data. The viability of the model is analysed by combining the conditions imposed by the Supernovae Ia and Baryonic Acoustic…
In this work we explore the dynamics of the generalized hybrid metric-Palatini theory of gravity in the weak-field, slow-motion regime. We start by introducing the equivalent scalar-tensor representation of the theory, which contains two scalar degrees of freedom, and perform a conformal transformation to the Einstein frame. Linear perturbations of the metric in a Minkowskian background are then studied for the metric and both scalar fields. The effective Newton constant and the PPN parameter $γ$ of the theory are extracted after transforming back to the (original) Jordan frame. Two particular…
In the Palatini action of general relativity the connection and the metric are treated as independent dynamical variables. Instead of assuming a relation between these quantities, the desired relation between them is derived through the Euler-Lagrange equations of the Palatini action. In this manuscript we construct an extended Palatini action, where we do not assume any a priori relationship between the connection, the covariant metric tensor, and the contravariant metric tensor. Instead we treat these three quantities as independent dynamical variables. We show that this action reproduces th…
The rapid advancement of gravitational wave astronomy in recent years has paved the way for the burgeoning development of black hole spectroscopy, which enhances the possibility of testing black holes by their quasinormal modes (QNMs). In this paper, the axial gravitational perturbations and the QNM frequencies of black holes in the hybrid metric-Palatini gravity (HMPG) are investigated. The HMPG theory is characterized by a dynamical scalar degree of freedom and is able to explain the late-time accelerating expansion of the universe without introducing any \textit{ad hoc} screening mechanism …
In this work, we explore cosmological sudden singularities arising in the dynamically equivalent scalar-tensor representation of generalized hybrid metric-Palatini gravity. Using a FLRW background, we show that the structure of the field equations prevents sudden singularities from arising at time derivatives of the scale factor of orders lower than four, but that they are allowed to appear for time derivatives of higher orders. Imposing an ansatz for the scale factor, we provide an explicit solution where these sudden singularities appear in the fourth-order time derivative of the scale facto…
A Palatini-type action for Einstein and Gauss-Bonnet gravity with non-trivial torsion is proposed. Three-form flux is incorporated via a deformation of the Riemann tensor, and consistency of the Palatini variational principle requires the flux to be covariantly constant and to satisfy a Jacobi identity. Studying gravity actions of third order in the curvature leads to a conjecture about general Palatini-Lovelock-Cartan gravity. We point out potential relations to string-theoretic Bianchi identities and, using the Schouten-Nijenhuis bracket, derive a set of Bianchi identities for the non-geomet…
In this work we will explore $U(1)$ local cosmic string solutions in the context of the generalized hybrid metric-Palatini theory of gravity in its scalar-tensor representation. Using a general static cylindrically symmetric metric to find the dynamical equations for this particular case, we will simplify the equations by imposing boost invariance along $t$ and $z$ directions. The strings properties are determined by both scalar fields and by the effective potential, function of the scalar fields. While for some forms of the potential, the dynamical equations can be solved exactly, for more ge…
The so-called hybrid metric-Palatini theory of gravity (HMPG), proposed in 2012 by T. Harko et al., is known to successfully describe both local (solar-system) and cosmological observations. This paper gives a complete description of static, spherically vacuum solutions of HMPG in the simplest case where its scalar-tensor representation has a zero scalar field potential $V(ϕ)$, and both Riemannian ($R$) and Palatini ($\cal R$) Ricci scalars are zero. Such a scalar-tensor theory coincides with general relativity with a phantom conformally coupled scalar field as a source of gravity. Generic asy…
Wormhole solutions in a generalized hybrid metric-Palatini matter theory, given by a gravitational Lagrangian $f\left(R,\cal{R}\right)$, where $R$ is the metric Ricci scalar, and $\mathcal{R}$ is a Palatini scalar curvature defined in terms of an independent connection, and a matter Lagrangian, are found. The solutions are worked in the scalar-tensor representation of the theory, where the Palatini field is traded for two scalars, $φ$ and $ψ$, and the gravitational term $R$ is maintained. The main interest in the solutions found is that the matter field obeys the null energy condition (NEC) ev…
We compare the metric and the Palatini formalism to obtain the Einstein equations in the presence of higher-order curvature corrections that consist of contractions of the Riemann tensor, but not of its derivatives. We find that there is a class of theories for which the two formalisms are equivalent. This class contains the Palatini version of Lovelock theory, but also more Lagrangians that are not Lovelock, but respect certain symmetries. For the general case, we find that imposing the Levi-Civita connection as an Ansatz, the Palatini formalism is contained within the metric formalism, in th…
It is shown that the Kerr solution exists in the generalized hybrid metric-Palatini gravity theory and that for certain choices of the function $f(R,\mathcal R)$ that characterizes the theory, the Kerr solution can be stable against perturbations on the scalar degree of freedom of the theory. We start by verifying which are the most general conditions on the function $f(R,\mathcal R)$ that allow for the general relativistic Kerr solution to also be a solution of this theory. We perform a scalar perturbation in the trace of the metric tensor, which in turn imposes a perturbation in both the Ric…
We consider static and cylindrically symmetric interior string type solutions in the scalar-tensor representation of the hybrid metric-Palatini modified theory of gravity. As a first step in our study, we obtain the gravitational field equations and further simplify the analysis by imposing Lorentz invariance along the $t$ and $z$ axes, which reduces the number of unknown metric tensor components to a single function $W^2(r)$. In this case, the general solution of the field equations can be obtained, for an arbitrary form of the scalar field potential, in an exact closed parametric form, with …
In this work, we explore the existence of traversable wormhole solutions supported by double gravitational layer thin-shells and satisfying the Null Energy Condition (NEC) throughout the whole spacetime, in a quadratic-linear form of the generalized hybrid metric-Palatini gravity. We start by showing that for a particular quadratic-linear form of the action, the junction conditions on the continuity of the Ricci scalar $R$ and the Palatini Ricci scalar $\mathcal R$ of the theory can be discarded without the appearance of undefined distribution terms in the field equations. As a consequence, a …
We investigate the nature of additional scalar degrees of freedom contained in extended hybrid metric-Palatini gravity, outlining the emergence of two coupled dynamical scalar modes. In particular, we discuss the weak field limit of the theory, both in the static case and from a gravitational waves perspective. In the first case, performing an analysis at the lowest order of the post parameterized Newtonian (PPN) structure of the model, we stress the settling of Yukawa corrections to the Newtonian potential. In this respect, we show that one scalar field can have long range interactions and us…
We discuss static, cylindrically symmetric vacuum solutions of hybrid metric-Palatini gravity (HMPG), a recently proposed theory that has been shown to successfully pass the local observational tests and to produce a certain progress in cosmology. We use HMPG in its well-known scalar-tensor representation. The latter coincides with general relativity containing, as a source of gravity, a conformally coupled scalar field $ϕ$ and a self-interaction potential $V(ϕ)$. The $ϕ$ field can be canonical or phantom, and accordingly the theory splits into canonical and phantom sectors. We seek solitonic …
The generalized hybrid metric-Palatini gravity is a theory of gravitation that has an action composed of a Lagrangian $f(R,\cal R)$, where $f$ is a function of the metric Ricci scalar $R$ and a new Ricci scalar $\cal R$ formed from a Palatini connection, plus a matter Lagrangian. This theory can be rewritten by trading the new geometric degrees of freedom of $f(R,\cal R)$ into two scalar fields, $φ$ and $ψ$, yielding an equivalent scalar-tensor theory. Given a spacetime theory, the next step is to find solutions. To construct solutions it is often necessary to know the junction conditions betw…
