Palatini Approach Research Articles

Higgs inflation model with non-minimal coupling in hybrid Palatini approach

In this paper, we propose a hybrid metric Palatini approach in which the Palatini scalar curvature is non minimally coupled to the scalar field. We derive Einstein's field equations, i.e., the equations of motion of the scalar field. Furthermore, the background and perturbative parameters are obtained by means of Friedmann equations in the slow roll regime. The analysis of cosmological perturbations allowed us to obtain the main inflationary parameters, e.g., the scalar spectral index and tensor to scalar ratio r. From this perspective, as an application of our analysis, we consider the Higgs field with quartic potential, which plays the inflaton role, and show that predictions of Higgs hybrid inflation are in good agreement with recent observational data [Astron. Astrophys. 641, 61 (2020)].

Dynamics of Cylindrical Collapse in Palatini Gravity

This research explores how filamentary objects behave when they collapse in the presence of exotic material. To accomplish this, we employ Palatini (R, T) theory as a candidate for exotic material. We derive the collapsing equation by enforcing the Darmois junction condition on the collapsed surface boundary. At this boundary, we obtain that the radial pressure is proportionate to the time‐dependent term of the field and is not zero. Lastly, we investigate the correlation between dark matter and gravitational waves and find that exotic terms disrupt the transmission of gravitational waves. It is worthwhile to mention here that our results (in both formalisms, metric approach and Palatini approach) reduce to (R) gravity and general relativity.

Modified gravity: A unified approach to metric-affine models

The starting point of this work is the original Einstein action, sometimes called the Gamma squared action. Continuing from our previous results, we study various modified theories of gravity following the Palatini approach. The metric and the connection will be treated as independent variables leading to generalized theories, which may contain torsion or non-metricity or both. Due to our particular approach involving the Einstein action, our setup allows us to formulate a substantial number of new theories not previously studied. Our results can be linked back to well-known models, such as Einstein–Cartan theory and metric-affine theories, and also links to many recently studied modified gravity models. In particular, we propose an Einstein–Cartan type modified theory of gravity, which contains propagating torsion, provided our function depends non-linearly on a boundary term. We also can state precise conditions for the existence of propagating torsion. Our work concludes with a brief discussion of cosmology and the role of cosmological torsion in our model. We find solutions with early-time inflation and late-time matter dominated behavior. No matter sources are required to drive inflation, and it becomes a purely geometrical effect.

Galactic rotation dynamics in a new f({mathcal {R}}) gravity model

We propose to test the viability of the recently introduced f(mathcal {R}) gravity model in the galactic scales. For this purpose we consider test particles moving in stable circular orbits around the galactic center. We study the Palatini approach of f(mathcal {R}) gravity via Weyl transformation, which is the frame transformation from the Jordan frame to the Einstein frame. We derive the expression of rotational velocities of test particles in the new f(mathcal {R}) gravity model. For the observational data of samples of high surface brightness and low surface brightness galaxies, we show that the predicted rotation curves are well fitted with observations, thus implying that this model can explain flat rotation curves of galaxies. We also study an ultra diffuse galaxy, AGC 242019 which has been claimed in literature to be a dark matter dominated galaxy similar to low surface brightness galaxies with a slowly rising rotation curve. The rotation curve of this galaxy also fits well with the model prediction in our study. Furthermore, we studied the Tully–Fisher relation for the entire sample of galaxies and found that the model prediction shows the consistency with the data.

Constant-roll inflation in modified f(R,phi ) gravity model using Palatini formalism

In this work, we study a constant-roll inflationary model in the Palatini formalism using modified gravity. Here our action consists a non-minimal coupling of a scalar field phi with Ricci scalar R in a general form of f(R,phi ). Using Palatini approach, we write its equivalent scalar-tensor form in the Einstein frame and then apply the constant-roll condition in the equation of motion for the inflaton field. Later the tensor-to-scalar ratio and the spectral index are calculated using the slow-roll parameters and the results obtained are matched with the Planck 2018 data. We found that the results agree nicely with the observations within the parameter regime under consideration.

Palatini approach and large-scale magnetogenesis

Large-scale magnetogenesis is analyzed within the Palatini approach when the gravitational action is supplemented by a contribution that is nonlinear in the Einstein-Hilbert term. While the addition of the nonlinear terms does not affect the scalar modes of the geometry during the inflationary phase, the tensor-to-scalar ratio is nonetheless suppressed. In this context it is plausible to have a stiff phase following the standard inflationary stage provided the potential has a quintessential form. The large-scale magnetic fields can even be a fraction of the nG over typical length scales of the order of the Mpc prior to the gravitational collapse of the protogalaxy.

Gauging scale symmetry and inflation: Weyl versus Palatini gravity

We present a comparative study of inflation in two theories of quadratic gravity with gauged scale symmetry: (1) the original Weyl quadratic gravity and (2) the theory defined by a similar action but in the Palatini approach obtained by replacing the Weyl connection by its Palatini counterpart. These theories have different vectorial non-metricity induced by the gauge field (w_mu ) of this symmetry. Both theories have a novel spontaneous breaking of gauged scale symmetry, in the absence of matter, where the necessary scalar field is not added ad-hoc to this purpose but is of geometric origin and part of the quadratic action. The Einstein-Proca action (of w_mu ), Planck scale and metricity emerge in the broken phase after w_mu acquires mass (Stueckelberg mechanism), then decouples. In the presence of matter (phi _1), non-minimally coupled, the scalar potential is similar in both theories up to couplings and field rescaling. For small field values the potential is Higgs-like while for large fields inflation is possible. Due to their R^2 term, both theories have a small tensor-to-scalar ratio (rsim 10^{-3}), larger in Palatini case. For a fixed spectral index n_s, reducing the non-minimal coupling (xi _1) increases r which in Weyl theory is bounded from above by that of Starobinsky inflation. For a small enough xi _1le 10^{-3}, unlike the Palatini version, Weyl theory gives a dependence r(n_s) similar to that in Starobinsky inflation, while also protecting r against higher dimensional operators corrections.

Thermodynamic behavior of time-dependent wormholes in Palatini f(R) gravity

In the frame work of Palatini approach to modified $f(R)$ theories of gravity, we attempt to investigate the thermodynamic behavior of time-dependent wormhole geometries. By considering an evolving wormhole spacetime, we find the field equations in Palatini $f(R)$ gravity. The energy density and pressure are redefined in order to satisfy the continuity equation. To discuss the thermodynamic behavior, an expression for the variation of total entropy is obtained. Then, we extend our discussions to apparent and event horizons of evolving wormholes. We employ the radius of apparent and event horizons to determine the validity of generalized second law (GSL) of thermodynamics which states that the variation of total entropy is non-negative.

Gödel and Gödel-type solutions in the Palatini f(R,T) gravity theory

The Palatini [Formula: see text] gravity theory is considered. The standard Einstein–Hilbert action is replaced by an arbitrary function of the Ricci scalar [Formula: see text] and of the trace [Formula: see text] of the energy-momentum tensor. In the Palatini approach, the Ricci scalar is a function of the metric and the connection. These two quantities, metric and connection, are taken as independent variables. Then, it is examined whether Palatini [Formula: see text] gravity theory allows solutions in which lead to violation of causality. The Gödel and Gödel-type spacetimes are considered. In addition, a critical radius, which permits to examine limits for violation of causality, is calculated. It is shown that, for different matter contents, noncausal solutions can be avoided in this Palatini gravitational theory.

General Slow-Roll Inflation in f(R) Gravity under the Palatini Approach

Slow-roll inflation is analyzed in the context of modified gravity within the Palatini formalism. As shown in the literature, inflation in this framework requires the presence of non-traceless matter; otherwise, it does not occur just as a consequence of the nonlinear gravitational terms of the action. Nevertheless, by including a single scalar field that plays the role of the inflaton, slow-roll inflation can be performed in these theories, where the equations lead to an effective potential that modifies the dynamics. We obtain the general slow-roll parameters and analyze a simple model to illustrate the differences introduced by the gravitational terms under the Palatini approach, and the modifications on the spectral index and the tensor to scalar ratio predicted by the model.

Palatini-Higgs inflation with nonminimal derivative coupling

The predictions of standard Higgs inflation in the framework of the metric formalism yield a tensor-to-scalar ratio $r\ensuremath{\sim}{10}^{\ensuremath{-}3}$ which lies well within the expected accuracy of near-future experiments $\ensuremath{\sim}{10}^{\ensuremath{-}4}$. When the Palatini formalism is employed, the predicted values of $r$ get highly suppressed $r\ensuremath{\sim}{10}^{\ensuremath{-}12}$ and consequently a possible nondetection of primordial tensor fluctuations will rule out only the metric variant of the model. On the other hand, the extremely small values predicted for $r$ by the Palatini approach constitute contact with observations a hopeless task for the foreseeable future. In this work, we propose a way to remedy this issue by extending the action with the inclusion of a generalized nonminimal derivative coupling term between the inflaton and the Einstein tensor of the form ${m}^{\ensuremath{-}2}(\ensuremath{\phi}){G}_{\ensuremath{\mu}\ensuremath{\nu}}{\ensuremath{\nabla}}^{\ensuremath{\mu}}\ensuremath{\phi}{\ensuremath{\nabla}}^{\ensuremath{\nu}}\ensuremath{\phi}$. We find that with such a modification, the Palatini predictions can become comparable with the ones obtained in the metric formalism, thus providing ample room for the model to be in contact with observations in the near future.

Reheating in R2 Palatini inflationary models

We consider $R^2$ inflation in the Palatini gravity assuming the existence of scalar fields, coupled to gravity in the most general manner. These theories, in the Einstein frame, and for one scalar field $h$, share common features with $K$ - inflation models. We apply this formalism for the study of popular inflationary models, whose potentials are monomials, $ V \sim h^{n} $, with $ n $ a positive even integer. We also study the Higgs model non-minimally coupled to gravity. Although these have been recently studied, in the framework of the Palatini approach, we show that the scalar power spectrum severely constrains these models. Although we do not propose a particular reheating mechanism, we show that the quadratic $ \sim h^2$ and the Higgs model can survive these constraints with a maximum reheating temperature as large as $ \sim 10^{15} \, GeV$, when reheating is instantaneous. However, this can be only attained at the cost of a delicate fine-tuning of couplings. Deviations from this fine-tuned values can still yield predictions compatible with the cosmological data, for couplings that lie in very tight range, giving lower reheating temperatures.

Varying the Horndeski Lagrangian within the Palatini approach

We analyse what happens when the Horndeski Lagrangian is varied within the Palatini approach by considering the metric and connection as independent variables. Assuming the connection to be torsionless, there can be infinitely many metric-affine versions LP of the original Lagrangian which differ from each other by terms proportional to the non-metricity tensor. After integrating out the connection, each LP defines a metric theory, which can either belong to the original Horndeski family, or it can be of a more general DHOST type, or it shows the Ostrogradsky ghost. We analyse in detail the subclass of the theory for which the equations are linear in the connection and find that its metric-affine version is ghost-free. We present a detailed classifications of homogeneous and isotropic cosmologies in these theories. Taking into consideration other pieces of the Horndeski Lagrangian which are non-linear in the connection leads to more complex metric-affine theories which generically show the ghost. In some special cases the ghost can be removed by carefully adjusting the non-metricity contribution, but it is unclear if this is always possible. Therefore, the metric-affine generalisations of the Horndeski theory can be ghost-free, but not all of them are ghost-free, neither are they the only metric-affine theories for a gravity-coupled scalar field which can be ghost-free.

Eddington-inspired-Born\u2013Infeld tensorial instabilities neutralized in a quantum approach

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 quantum treatment of the affine connection, or equivalently of its compatible metric, is able to rescue the model. We carry out such an analysis and conclude that from a quantum point of view such a Big Bang is unharmful. We expect therefore that the induced tensorial instability, caused by the Big Bang intrinsic to the affine connection, can be neutralized at the quantum level.

Nonsingular and ghost-free infinite derivative gravity with torsion

We present the most general quadratic curvature action with torsion including infinite covariant derivatives and study its implications around the Minkowski background via the Palatini approach. Provided the torsion is solely given by the background axial field, the metric and torsion are shown to decouple, and both of them can be made ghost and singularity free for a fermionic source.

F(R,∇μ1R,…,∇μ1…∇μnR) theories of gravity in Einstein frame: A higher order modified Starobinsky inflation model in the Palatini approach

In Cuzinatto et al. [Phys. Rev. D 93, 124034 (2016)], it has been demonstrated that theories of gravity in which the Lagrangian includes terms depending on the scalar curvature $R$ and its derivatives up to order $n$, i.e. $f\left(R,\nabla_{\mu}R,\nabla_{\mu_{1}}\nabla_{\mu_{2}}R,\dots,\nabla_{\mu_{1}}\dots\nabla_{\mu_{n}}R\right)$ theories of gravity, are equivalent to scalar-multitensorial theories in the Jordan frame. In particular, in the metric and Palatini formalisms, this scalar-multitensorial equivalent scenario shows a structure that resembles that of the Brans-Dicke theories with a kinetic term for the scalar field with $\omega_{0}=0$ or $\omega_{0}=-3/2$, respectively. In the present work, the aforementioned analysis is extended to the Einstein frame. The conformal transformation of the metric characterizing the transformation from Jordan's to Einstein's frame is responsible for decoupling the scalar field from the scalar curvature and also for introducing a usual kinetic term for the scalar field in the metric formalism. In the Palatini approach, this kinetic term is absent in the action. Concerning the other tensorial auxiliary fields, they appear in the theory through a generalized potential. As an example, the analysis of an extension of the Starobinsky model (with an extra term proportional to $\nabla_{\mu}R\nabla^{\mu}R$) is performed and the fluid representation for the energy-momentum tensor is considered. In the metric formalism, the presence of the extra term causes the fluid to be an imperfect fluid with a heat flux contribution; on the other hand, in the Palatini formalism the effective energy-momentum tensor for the extended Starobinsky gravity is that of a perfect fluid type. Finally, it is also shown that the extra term in the Palatini formalism represents a dynamical field which is able to generate an inflationary regime without a graceful exit.

Apparent Horizon and Gravitational Thermodynamics of Universe in the Eddington-Born-Infeld Theory

The thermodynamics of Universe in the Eddington-Born-Infeld (EBI) theory was restudied by utilizing the holographic-style gravitational equations that dominate the dynamics of the cosmical apparent horizon ΥA and the evolution of Universe. We started in rewriting the EBI action of the Palatini approach into the Bigravity-type action with an extra metric qμν. With the help of the holographic-style dynamical equations, we discussed the property of the cosmical apparent horizon ΥA including timelike, spacelike, and null characters, which depends on the value of the parameter of state wm in EBI Universe. The unified first law for the gravitational thermodynamics and the total energy differential for the open system enveloped by ΥA in EBI Universe were obtained. Finally, applying the positive-heat-out sign convention, we derived the generalized second law of gravitational thermodynamics in EBI Universe.

Palatini wormholes and energy conditions from the prism of general relativity

Wormholes are hypothetical shortcuts in spacetime that in general relativity unavoidably violate all of the pointwise energy conditions. In this paper, we consider several wormhole spacetimes that, as opposed to the standard designer procedure frequently employed in the literature, arise directly from gravitational actions including additional terms resulting from contractions of the Ricci tensor with the metric, and which are formulated assuming independence between metric and connection (Palatini approach). We reinterpret such wormhole solutions under the prism of General Relativity and study the matter sources that thread them. We discuss the size of violation of the energy conditions in different cases and how this is related to the same spacetimes when viewed from the modified gravity side.

A relativistic description of MOND using the Palatini formalism in an extended metric theory of gravity

We construct a relativistic metric description of MOND using the Palatini formalism following the \( f(\chi)=\chi^b \) description of \citet{mendozatula}. We show that in order to recover the non-relativistic MOND regime where, for circular orbits the Tully-Fisher law replaces Kepler's third law, the value of the parameter $ b = 3/2 $, which is coincident with the value found using a pure metric formalism Capozziello et al. (2011). Unlike the pure metric formalism, which yields 4th order field equations, the Palatini approach yields second order field equations, which is a desirable requirement from a theoretical perspective. Thus, the phenomenology associated to astrophysical phenomena with Tully-Fisher scalings can be accounted for using this proposal, without the need to introduce any non-baryonic dark matter particles.

Chaplygin gas of Tachyon Nature Imposed by Noether Symmetry and constrained via H(z) data

An action of general form is proposed for a Universe containing matter, radiation and dark energy. The latter is interpreted as a tachyon field non-minimally coupled to the scalar curvature. The Palatini approach is used when varying the action so the connection is given by a more generic form. Both the self-interaction potential and the non-minimally coupling function are obtained by constraining the system to present invariability under global point transformation of the fields (Noether Symmetry). The only possible solution is shown to be that of minimal coupling and constant potential (Chaplygin gas). The behavior of the dynamical properties of the system is compared to recent observational data, which infers that the tachyon field must indeed be dynamical.