arXiv subjects

Shahab Shahidi

Publications and source records attributed to Shahab Shahidi.

At least 19 recordsLinked to original sources

arXiv2026

New generalization of the Barboza-Alcaniz parametrization of Dark energy

A generalization of the Barboza-Alcaniz parametrization of dark energy is proposed. This is a three-parameter model which can resolve the shortcomings of the Barboza-Alcaniz behavior at future times. We show that cosmological data favor the new parametrization over both the Barboza-Alcaniz model and $\Lambda$CDM. We also consider the cosmological implications of the model and show that the qualitative behavior mimics to the original Barboza-Alcaniz model, with a slightly smaller acceleration rate.

gr-qc↗

arXiv2026

Dark energy and accelerating cosmological evolution in a Universe with a Weylian boundary

We investigate the influence of boundary terms in gravitational field theories, by considering that in the Einstein-Hilbert action the boundary can be described by a non-metric Weyl-type geometry. The gravitational action and the the field equations, are thus generalized to include new geometrical terms, coming from the non-metric nature of the boundary, and depending on the Weyl vector, and its covariant derivatives. The field equations obtained within this framework generalize the standard Einstein equations by including in their mathematical structure the Weyl vector, and its covariant derivatives. As an applications of the general formalism we investigate the cosmological evolution in a flat FLRW geometry. We obtain the generalized Friedmann equations, which contain extra terms depending on the Weyl vector and its derivatives, arising due to the presence of the Weylian boundary, and which describe an effective, time dependent dark energy. By imposing to the dark energy an equation of state parameter of the Barboza-Alcaniz type, the Friedmann equations can be solved numerically. We compare the predictions of the Weylian boundary gravitational theory with late-time observational data and the predictions of the $Λ$CDM paradigm. Our results show that the Weylian boundary cosmological models give a good description of the observational data, and they can reproduce almost exactly the predictions of the $Λ$CDM paradigm. Hence, the extension of gravitational theories through the addition of Weylian boundary terms, in which dark energy has a purely geometric origin, emerges as a viable alternative to standard general relativity.

gr-qc↗

arXiv2026

Dark energy and a new realization of the matter Lagrangian

A new realization of the matter Lagrangian is introduced which models the dark energy component as a non-standard combination of thermodynamics quantities of the baryonic matter. We will prove that the present realization is independent of existing models with matter-geometry couplings and has a property that the energy-momentum tensor of both baryonic matter and dark energy is conserved separately. We further show that two possible choices of the matter Lagrangian in the $Λ$CDM model are not totally equivalent and investigate the background and perturbative constraints on the form of matter Lagrangian. We will also investigate cosmological implications of a test model with logarithmic DE and obtain the model parameters by confronting the model with observational data on the cosmic chronometers, Pantheon$^+$ and $fσ_8$ datasets. We will also explain in details the predictions of the model on the late time behavior of the universe and compare the result with $Λ$CDM model.

gr-qc↗

arXiv2025

Cosmology in generalized hybrid metric-Palatini with matter-geometry coupling

Cosmological implications of a class of hybrid metric-Palatini gravity with a non-minimal matter-geometry coupling is considered. The theory contains a metric curvature tensor, together with a curvature tensor constructed from an independent affine connection. We will show that the model could be written as a bi-scalar-tensor gravity with a non-minimal coupling between matter sector and a scalar field. The theory will then be confronted with observational data from Cosmic Chronometers, BAO dataset from DESI and the Pantheon$^+$ dataset. We will show that the theory could be a good alternative to the $Λ$CDM model with the difference that the conservation of the baryonic matter sector holds only at the background level. The statefinder analysis will also be applied to the theory and it is observed that the DE behavior of the theory exhibits a quintessence to phantom transition occurs at redshifts around $z\approx0.86$.

gr-qc↗

arXiv2025

Cosmological implications of hybrid metric-Palatini $f(\mathcal{R},\mathcal{R}_{μν}\mathcal{R}^{μν})$ gravity

The hybrid metric-Palatini gravity with Lagrangian density $L =R+f(\mathcal{R},\mathcal{R}_{μν}\mathcal{R}^{μν})$ is considered, where $R$ is the metric Ricci scalar and $\mathcal{R}_{μν}$ is the Palatini Ricci tensor. Contrary to the standard hybrid metric-Palatini theory, because of the term $\mathcal{R}_{μν}\mathcal{R}^{μν}$ in the action, the model can not be analytically transformed to a scalar-tensor theory. However, on top of a maximally symmetric space-times like the FRW universe, there is a way to solve for a metric compatible connection which we will follow in this paper. The cosmological implications of the resulting model will then be fully considered. The best fit values of the model and cosmological parameters will be obtained by confronting the model with the recent observational data on the Hubble parameter. We will see that the observational data can be explained very good in this model, but, significant deviations from the standard $Λ$CDM model could be seen in derivatives of the Hubble parameter $q$, $j$ and $s$. We will perform a statefinder analysis for the model and show that its behavior differs from that of the $Λ$CDM model. Also, we will consider the recently proposed $Om$ diagnostics to categorize the dark energy type of the model and obtain the $ω$-varying alternative of the model that mimics the Hubble flow.

gr-qc↗

arXiv2025

From Barthel Randers Kropina Geometries to the Accelerating Universe: A Brief Review of Recent Advances in Finslerian Cosmology

We review recent developments in cosmological models based on Finsler geometry and extensions of general relativity within this framework. Finsler geometry generalizes Riemannian geometry by allowing the metric tensor to depend on position and an additional internal degree of freedom, typically represented by a vector field at each point of the spacetime manifold. We explore whether Finsler-type geometries can describe gravitational interaction and cosmological dynamics. In particular, we examine the Barthel connection and $(α, β)$ geometries, where $α$ is a Riemannian metric and $β$ is a one-form. For a specific construction of $β$, the Barthel connection coincides with the Levi-Civita connection of the associated Riemann metric. We review gravitational field and cosmological evolution in three geometries: Barthel-Randers ($F = α+ β$), Barthel-Kropina ($F = α^2 β$), and the conformally transformed Barthel-Kropina geometry. After presenting the mathematical foundations of Finslerian-type modified gravity theories, we derive generalized Friedmann equations in these geometries assuming a Friedmann-Lemaître-Robertson-Walker type metric. We also present the matter-energy balance equations, interpreting them from the perspective of thermodynamics with particle creation. The cosmological properties of Barthel-Randers and Barthel-Kropina models are explored in detail. The additional geometric terms in these models can be interpreted as an effective dark energy component, generating an effective cosmological constant. Several cosmological solutions are compared with observational data (Cosmic Chronometers, Type Ia Supernovae, Baryon Acoustic Oscillations) using MCMC analysis. A comparison with the $Λ$CDM model shows that Finslerian models fit observational data well, suggesting they offer a viable alternative to general relativity.

gr-qc↗

arXiv2025

Matter really does matter, or Why $f(R,{\rm Matter})$ type theories are significant for gravitational physics and cosmology

In a recent paper (Lacombe, Mukohyama, and Seitz, JCAP {\bf 2024}, 05, 064 (2024)), the authors provided an in-depth analysis of a class of modified gravity theories, generally called $f(R,{\rm Matter})$ theories, which assume the existence of a non-minimal coupling between geometry and matter. It was argued that if the matter sector consists of Standard Model particles, then these theories suffer from the presence of ghosts, or are just scalar/vector-tensor theories. Hence, the relevance of these theories for cosmology was questioned. It is the goal of the present work to carefully analyze, discuss, and assess the line of arguments proposed in Lacombe et al. JCAP {\bf 2024}, 05, 064 (2024). After a qualitative critical discussion of the five general arguments proposed for the validity of a gravitational theory, we present the theoretical foundations of the $f(R,{\rm Matter})$ theories, including their possible relations with quantum gravity, and discuss in detail the role of matter. The matter source discussed in Lacombe et al., consisting predominantly of a massless scalar field, is extremely restrictive, and rather irrelevant for cosmology and the description of the observational data. We also devote a detailed discussion of the problem of the energy scales of the $f(R,{\rm Matter})$ theories. To test the observational relevance of this type of theories we present the comparison of a simple theoretical model with a small set of observational data and with the $Λ$CDM paradigm. We conclude by pointing out that the analysis of Lacombe et al., JCAP {\bf 2024}, 05, 064 (2024), even very useful for the understanding of some limited aspects of the $f(R,{\rm Matter})$ theories, and of their theoretical foundations, cannot be considered as a valid or definite criticism of these approaches to gravity.

gr-qc↗

arXiv2025

Mimetic Weyl geometric gravity

We consider a mimetic type extension of the Weyl geometric gravity theory, by assuming that the metric of the space-time manifold can be parameterized in terms of a scalar field, called the mimetic field. The action of the model is obtained by starting from a conformally invariant gravitational action, constructed, in Weyl geometry, from the square of the Weyl scalar, the strength of the Weyl vector, and an effective matter term, respectively. after linearizing the action in the Weyl scalar by introducing an auxiliary scalar field, we include the mimetic field, constructed from the same auxiliary scalar field used to linearize the action, via a Lagrange multiplier. The conformal invariance of the action is maintained by imposing the trace condition on the effective matter energy-momentum tensor, built up from the ordinary matter Lagrangian, and some specific functions of the Weyl vector, and the scalar field, respectively, thus making the matter sector of the action conformally invariant. We investigate the cosmological implications of the Mimetic Weyl geometric gravity by considering the dynamics of an isotropic and homogeneous FRW Universe. The generalized Friedmann equations of the model are derived, and their solutions are obtained numerically for a dust filled Universe. Moreover, we perform a detailed comparison of the predictions of the considered model with a set of observational data for the Hubble function, and with the results of the $Λ$CDM standard paradigm. Our results indicate that the present model give a good description of the observational data, and they reproduce almost exactly the predictions of the $Λ$CDM scenario. Hence, Mimetic Weyl geometric gravity can be considered a viable alternative to the standard approaches to cosmology, and to the gravitational phenomena.

gr-qc↗

arXiv2024

The first variation of the matter energy-momentum tensor with respect to the metric, and its implications on modified gravity theories

The first order variation of the matter energy-momentum tensor $T_{μν}$ with respect to the metric tensor $g^{αβ}$ plays an important role in modified gravity theories with geometry-matter coupling, and in particular in the $f(R,T)$ modified gravity theory. We obtain the expression of the variation $δT_{μν}/δg^{αβ}$ for the baryonic matter described by an equation given in a parametric form, with the basic thermodynamic variables represented by the particle number density, and by the specific entropy, respectively. The first variation of the matter energy-momentum tensor turns out to be independent on the matter Lagrangian, and can be expressed in terms of the pressure, the energy-momentum tensor itself, and the matter fluid four-velocity. We apply the obtained results for the case of the $f(R,T)$ gravity theory, where $R$ is the Ricci scalar, and $T$ is the trace of the matter energy-momentum tensor, which thus becomes a unique theory, also independent on the choice of the matter Lagrangian. A simple cosmological model, in which the Hilbert-Einstein Lagrangian is generalized through the addition of a term proportional to $T^n$ is considered in detail, and it is shown that it gives a very good description of the observational values of the Hubble parameter up to a redshift of $z\approx 2.5$.

gr-qc↗

arXiv2024

Cosmological implications of the Weyl geometric gravity theory

We consider cosmological implications of the Weyl geometric gravity theory. The basic action of the model is obtained from the simplest conformally invariant gravitational action, constructed, in Weyl geometry, from the square of the Weyl scalar, the strength of the Weyl vector, and a matter term, respectively. The total action is linearized in the Weyl scalar by introducing an auxiliary scalar field. To maintain the conformal invariance of the action the trace condition is imposed on the matter energy-momentum tensor, thus making the matter sector of the action conformally invariant. The field equations are derived by varying the action with respect to the metric tensor, the Weyl vector field, and the scalar field, respectively. We investigate the cosmological implications of the theory, and we obtain first the cosmological evolution equations for a flat, homogeneous and isotropic geometry, described by Friedmann-Lemaitre-Robertson-Walker metric, which generalize the Friedmann equations of standard general relativity. In this context we consider two cosmological models, corresponding to the vacuum state, and to the presence of matter described by a linear barotropic equation of state. In both cases we perform a detailed comparison of the predictions of the theory with the cosmological observational data, and with the standard $Λ$ CDM model. By assuming that the presence of the Weyl geometric effects induce small perturbations in the homogeneous and isotropic cosmological background, and that the anisotropy parameter is small, the equations of the cosmological perturbations due to the presence of the Weyl geometric effects are derived. The time evolution of the metric and matter perturbations are explicitly obtained. So, if Weyl geometric effects are present, the Universe would acquire some anisotropic characteristics, and its geometry will deviate from the standard FLRW one.

gr-qc↗

arXiv2023

Reply to Comment on "Dark matter as a Weyl geometric effect"

In a recent Comment on the paper "Dark matter as a Weyl geometric effect", by Burikham et al., Phys. Rev. D 107, 064008 (2023), posted on arxiv. org as eprint arXiv:2306.11926, it was claimed that the exact solution found in the above mentioned paper by Burikham et al. "is wrong". In this Reply to the Comment we present, in a clear and comprehensive way, a step by step derivation of the exact solution of the vacuum static spherically symmetric field equations of the Weyl geometric gravity theory, and we show that, contrary to the claims in arXiv:2306.11926, the obtained solution is correct, and it satisfies all the equations of motion of the basic theory. Hence, it can be considered as a viable alternative model for the explanation of the behavior of the galactic rotation curves, without invoking the presence of dark matter.

gr-qc↗

arXiv2023

Dark matter as a Weyl geometric effect

We investigate the possibility that the observed behavior of test particles outside galaxies, which is usually explained by assuming the existence of dark matter, is the result of the dynamical evolution of particles in a Weyl type geometry, and its associated conformally invariant Weyl geometric quadratic gravity. As a first step in our investigations we write down the simplest possible conformally invariant gravitational action, constructed in Weyl geometry, and containing the Weyl scalar, and the strength of the Weyl vector only. By introducing an auxiliary scalar field, the theoretical model can be reformulated in the Riemann geometry as scalar-vector-tensor theory, containing a scalar field, and the Weyl vector, respectively. The field equations of the theory are derived in the metric formalism, in the absence of matter. A specific static, spherically symmetric model, in which the Weyl vector has only a radial component, is considered. In this case, an exact analytic solution of the gravitational field equations can be obtained. The behavior of the galactic rotation curves is also considered in detail, and it is shown that an effective geometric mass term, with an associated density profile, can also be introduced. Three particular cases, corresponding to some specific functional forms of the Weyl vector, are also investigated. A comparison of the model with a selected sample of galactic rotation curves is also performed when an explicit breaking of conformal invariance is introduced, which allows the fix of the numerical values of the free parameters of the model. Our results show that Weyl geometric models can be considered as a viable theoretical alternative to the dark matter paradigm.

gr-qc↗

arXiv2022

Black hole solutions in the quadratic Weyl conformal geometric theory of gravity

We consider numerical black hole solutions in the Weyl conformal geometry, and its associated conformally invariant Weyl quadratic gravity. In this model Einstein gravity (with a positive cosmological constant) is recovered in the spontaneously broken phase of Weyl gravity, after the Weyl gauge field ($ω_μ$) becomes massive through a Stueckelberg mechanism, and it decouples. As a first step in our investigations we write down the conformally invariant gravitational action, containing a scalar degree of freedom, and the Weyl vector. The field equations are derived from the variational principle in the absence of matter. By adopting a static spherically symmetric geometry, the vacuum field equations for the gravitational, scalar, and Weyl fields are obtained. After reformulating the field equations in a dimensionless form, and by introducing a suitable independent radial coordinate, we obtain their solutions numerically. We detect the formation of a black hole from the presence of a Killing horizon for the timelike Killing vector in the metric tensor components, indicating the existence of the singularity in the metric. Several models, corresponding to different functional forms of the Weyl vector, are considered. An exact black hole model, corresponding to a Weyl vector having only a radial spacelike component, is also obtained. The thermodynamic properties of the Weyl geometric type black holes (horizon temperature, specific heat, entropy and evaporation time due to Hawking luminosity) are also analyzed in detail.

gr-qc↗

arXiv2022

Palatini formulation of the conformally invariant $f\left(R, L_m\right)$ gravity theory

We investigate the field equations of the conformally invariant models of gravity with curvature-matter coupling, constructed in Weyl geometry, by using the Palatini formalism. We consider the case in which the Lagrangian is given by the sum of the square of the Weyl scalar, of the strength of the field associated to the Weyl vector, and a conformally invariant geometry-matter coupling term, constructed from the matter Lagrangian and the Weyl scalar. After substituting the Weyl scalar in terms of its Riemannian counterpart, the quadratic action is defined in Riemann geometry, and involves a nonminimal coupling between the Ricci scalar and the matter Lagrangian. For the sake of generality, a more general Lagrangian, in which the Weyl vector is nonminmally coupled with an arbitrary function of the Ricci scalar, is also considered. By varying the action independently with respect to the metric and the connection, the independent connection can be expressed as the Levi-Civita connection of an auxiliary, Ricci scalar and Weyl vector dependent metric, which is related to the physical metric by means of a conformal transformation. The field equations are obtained in both the metric and the Palatini formulations. The cosmological implications of the Palatini field equations are investigated for three distinct models corresponding to different forms of the coupling functions. A comparison with the standard $Λ$CDM model is also performed, and we find that the Palatini type cosmological models can give an acceptable description of the observations.

gr-qc↗

arXiv2022

Anisotropy in constraint 4D Gauss-Bonnet gravity

Recently a new 4D Einstein-Gauss-Bonnet theory has been introduced \textbf{[Phys. Rev. Lett. 124 (2020) 081301]} with a serious debate that it does not possess a covariant equation of motion in $4D$. This feature, makes impossible to consider non-symetric space-times in this model, such as anisotropic cosmology. In this note, we will present a new proposal to make this happen, by introducing a Lagrange multiplier to the action which eliminates the higher dimensional term from the equation of motion. The theory has then a covariant $4D$ equation of motion which is useful to study the less symmetric metrics. On top of FRW universe, the constraint theory is equivalent to the original $4D$ Einstein-Gauss-Bonnet gravity. We will then consider the anisotropic cosmology of the model and compare the theory with observational data. We will see that the theory becomes non-conservative and the matter density abundance falls more rapidly at larger redshifts compared to the conservative matter sources.

gr-qc↗

arXiv2022

Coupling matter and curvature in Weyl geometry: conformally invariant $f\left(R,L_m\right)$ gravity

We investigate the coupling of matter to geometry in conformal quadratic Weyl gravity, by assuming a coupling term of the form $L_m\tilde{R}^2$, where $L_m$ is the ordinary matter Lagrangian, and $\tilde{R}$ is the Weyl scalar. The coupling explicitly satisfies the conformal invariance of the theory. By expressing $\tilde{R}^2$ with the help of an auxiliary scalar field and of the Weyl scalar, the gravitational action can be linearized, leading in the Riemann space to a conformally invariant $f\left(R,L_m\right)$ type theory, with the matter Lagrangian nonminimally coupled to the Ricci scalar. We obtain the gravitational field equations of the theory, as well as the energy-momentum balance equations. The divergence of the matter energy-momentum tensor does not vanish, and an extra force, depending on the Weyl vector, and matter Lagrangian is generated. The thermodynamic interpretation of the theory is also discussed. The generalized Poisson equation is derived, and the Newtonian limit of the equations of motion is considered in detail. The perihelion precession of a planet in the presence of an extra force is also considered, and constraints on the magnitude of the Weyl vector in the Solar System are obtained from the observational data of Mercury. The cosmological implications of the theory are also considered for the case of a flat, homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker geometry, and it is shown that the model can give a good description of the observational data for the Hubble function up to a redshift of the order of $z\approx 3$.

gr-qc↗

arXiv2022

Non-minimal geometry-matter couplings in Weyl-Cartan space-times: $f(R,T,Q,T_m)$ gravity

We consider an extension of standard General Relativity in which the Hilbert-Einstein action is replaced by an arbitrary function of the Ricci scalar, nonmetricity, torsion, and the trace of the matter energy-momentum tensor. By construction, the action involves a non-minimal coupling between matter and geometry. The field equations of the model are obtained, and they lead to the nonconservation of the matter energy-momentum tensor. A thermodynamic interpretation of the nonconservation of the energy-momentum tensor is also developed in the framework of the thermodynamics of the irreversible processes in open systems. The Newtonian limit of the theory is considered, and the generalized Poisson equation is obtained in the low velocity and weak fields limits. The nonmetricity, the Weyl vector, and the matter couplings generate an effective gravitational coupling in the Poisson equation. We investigate the cosmological implications of the theory for two different choices of the gravitational action, corresponding to an additive and a multiplicative algebraic structure of the function $f$, respectively. We obtain the generalized Friedmann equations, and we compare the theoretical predictions with the observational data. \te{We find that the cosmological models can give a good descriptions of the observations up to a redshift of $z=2$, and, for some cases, up to a redshift of $z=3$.

gr-qc↗

arXiv2021

Cosmological evolution and dark energy in osculating Barthel-Randers geometry

We consider the cosmological evolution in an osculating point Barthel-Randers type geometry, in which to each point of the space-time manifold an arbitrary point vector field is associated. This Finsler type geometry is assumed to describe the physical properties of the gravitational field, as well as the cosmological dynamics. For the Barthel-Randers geometry the connection is given by the Levi-Civita connection of the associated Riemann metric. The generalized Friedmann equations in the Barthel-Randers geometry are obtained by considering that the background Riemannian metric in the Randers line element is of Friedmann-Lemaitre-Robertson-Walker type. The matter energy balance equation is derived, and it is interpreted from the point of view of the thermodynamics of irreversible processes in the presence of particle creation. The cosmological properties of the model are investigated in detail, and it is shown that the model admits a de Sitter type solution, and that an effective cosmological constant can also be generated. Several exact cosmological solutions are also obtained. A comparison of three specific models with the observational data and with the standard $Λ$CDM model is also performed by fitting the observed values of the Hubble parameter, with the models giving a satisfactory description of the observations.

gr-qc↗