We investigate a cosmological model within the framework of [Formula: see text] gravity by adopting the linear functional form [Formula: see text], where [Formula: see text] denotes the matter-geometry coupling constant. Working within a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) background, we derive the modified Friedmann equations and subsequently obtain an analytical expression for the Hubble parameter by employing a linear redshift-dependent parameterization of the equation of state (EOS), [Formula: see text]. The model parameters are constrained through a comprehensive multi-dataset observational analysis utilizing cosmic chronometer (CC) measurements, Type Ia supernovae data from the Pantheon+ and Union 3.0 compilations, baryon acoustic oscillation (BAO) data from the DESI survey, and cosmic microwave background (CMB) distance priors derived from Planck 2018 observations. Best-fit parameter values are extracted via [Formula: see text] minimization over the combined dataset as well as individual dataset separately. We explore the cosmological evolution of the model through several physical diagnostics, including the effective energy density, cosmic pressure, EOS parameter, and deceleration parameter. Higher order geometrical diagnostics, such as the statefinder pair [Formula: see text], the jerk parameter [Formula: see text], and the [Formula: see text] diagnostic, all are utilized to differentiate the presented model from the standard [Formula: see text]CDM framework. Our critical analysis describes that the model successfully could exhibits the transition from an early decelerating phase to the present epoch of accelerated expansion of the Universe, with an EOS parameter lying within the quintessence domain. An overall testing of the energy conditions confirms their validity in the allowed parameter space.
We investigate optical observables, neutral-particle dynamics, and epicyclic frequencies in the spacetime of spherically symmetric black holes sourced by the ModMax and phantom ModMax, or Mod(A)Max, nonlinear electrodynamics sectors. The metric contains an effective charge contribution governed by the electric charge [Formula: see text], the ModMax parameter [Formula: see text], and the discrete branch parameter [Formula: see text]. This structure is simple enough to allow analytical progress, but rich enough to generate two qualitatively different phenomenological regimes. We provide a unified analysis of null geodesics, massive circular motion, and small oscillations about stable orbits. For photons, we derive the effective potential, the photon-sphere radius, the shadow radius, the weak-field deflection angle, and representative trajectories. For neutral massive particles, we obtain the Hamiltonian effective potential, the effective radial force, the specific energy and angular momentum of circular equatorial orbits, and the innermost stable circular orbit. We then compute the Keplerian, radial, and vertical epicyclic frequencies, together with the periastron precession frequency, and discuss their relevance for QPO phenomenology. The main result is a coherent branch-dependent pattern: the ordinary ModMax sector tends to shrink the photon sphere, shadow, and ISCO scales as the effective charge grows, whereas the phantom Mod(A)Max sector enlarges these scales and shifts stable circular motion outward. The parameter [Formula: see text] exponentially suppresses the effective charge contribution and drives both branches toward the Schwarzschild limit. This combined optical–dynamical treatment identifies the parameter combination [Formula: see text] as the key quantity controlling the deviations and provides a baseline for future constraints from black-hole shadows, accretion-disk observables, and QPO measurements.
In this paper, we investigate the thermodynamic and optical properties of Einstein–Born–Infeld–Anti–de Sitter (EBI-AdS) black holes (BHs). Our study derives the Hawking temperature using the standard surface gravity method and examines quantum corrections through both the Generalized Uncertainty Principle (GUP) and exponential entropy modifications, revealing enhanced thermal radiation and possible remnant formation scenarios. The gravitational redshift analysis disentangles the contributions of mass, cosmological constant, electromagnetic charge, and Born–Infeld (BI) nonlinear corrections, with the latter scaling as [Formula: see text] and therefore becoming significant only in the near-horizon regime. [Formula: see text]Using the Gauss–Bonnet theorem, we compute the weak deflection angle of light in both vacuum and plasma media and show that dispersive effects may either enhance or suppress nonlinear electrodynamic signatures depending on the observational setup. In the extended phase-space formalism, where the BH mass is interpreted as enthalpy, the thermodynamic analysis reveals phase structures characterized by heat-capacity transitions between positive and negative regions, indicating local stability and instability depending on the parameter space. We further analyze BH heat engines operating in rectangular cycles and find efficiencies in the range [Formula: see text]–[Formula: see text], corresponding to approximately [Formula: see text]–[Formula: see text] of the associated Carnot efficiencies, consistent with other AdS BH systems. [Formula: see text]A comparison with Johnson’s framework shows that BI-induced corrections to the heat-engine efficiency are typically of order [Formula: see text] for standard parameter choices, although they become appreciable in the strong-field regime where [Formula: see text] in Planck units. Finally, the plasma-lensing analysis reveals frequency-dependent refractive modifications encoded in the plasma parameter, thereby offering an additional observational channel for testing nonlinear electromagnetic effects in black-hole environments.
We study the late-time expansion of the universe in the framework of curvature-matter coupling gravity by considering the model [Formula: see text], where [Formula: see text], [Formula: see text], and [Formula: see text] are free model parameters. We assume a spatially flat FLRW universe filled with pressureless matter, derive the modified Friedmann equations, and obtain an exact analytical solution for the Hubble parameter. The solution approaches a de Sitter phase in the asymptotic future for [Formula: see text]. The model parameters are constrained through a Bayesian Markov Chain Monte Carlo analysis using cosmic chronometer [Formula: see text] measurements, the Pantheon+SH0ES Type Ia supernova compilation, DESI DR2 baryon acoustic oscillation observations, and their joint combination. The [Formula: see text] and DESI DR2 datasets favor values of the Hubble constant compatible with early- and intermediate-Universe measurements, whereas Pantheon+SH0ES prefers a larger value consistent with local distance-ladder observations. The joint analysis yields [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], indicating that the model remains close to the general relativistic limit while allowing a small curvature-matter coupling. Moreover, we reconstruct the cosmographic parameters [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], which show the expected transition from decelerated to accelerated expansion, remain consistent with a [Formula: see text]CDM-like expansion history, and converge to constant values in the asymptotic future. These results show that a simple curvature-matter coupling presents a reasonable description of the late-time cosmic expansion while remaining compatible with current cosmological observations.
In this work, we study particle production in an inflationary scenario, focusing on the geometric mechanism induced by spacetime inhomogeneities. We investigate the effect of a non-minimal coupling between the inflaton and the Ricci scalar for a quadratic benchmark potential. In the weak-coupling regime, we compare negative, vanishing, and positive values of [Formula: see text]. For the adopted parameters, nonzero coupling enhances the squared momentum-space pair-production amplitude relative to the minimally coupled case.
We analyze two vacuum decay cosmological models using baryon acoustic oscillation (BAO) measurements from DESI DR2 in combination with cosmic microwave background (CMB), cosmic chronometer (CC), and multiple Type Ia supernova samples (Pantheon[Formula: see text], DES-Dovekie, and Union3). In contrast to previous DESI DR1-based studies, which reported moderate to strong evidence against the non-interacting case, our results show that DESI DR2 substantially weakens this level of exclusion. For both vacuum decay models, the interaction parameter is consistent with zero at a significance level of less than [Formula: see text] for all combinations of datasets considered, implying that the non-interacting scenario cannot be ruled out. We further examine the implications for cosmological parameters. While the vacuum decay models mildly shift the Hubble parameter toward higher values compared to [Formula: see text]CDM, leading to a modest alleviation of the [Formula: see text] tension, they do not fully resolve the discrepancy with the SH0ES measurement. The matter density parameter [Formula: see text], as well as the baryon and radiation density parameters, remain consistent across models within [Formula: see text]. Model comparison using [Formula: see text] shows only weak preference ([Formula: see text]) for the vacuum decay models, while Bayesian evidence remains inconclusive and, in most cases, mildly favors [Formula: see text]CDM. Our analysis demonstrates that the DESI DR2 data substantially reduce the previously reported exclusion of the non-interacting scenario in vacuum decay models, bringing the results into consistency with the standard non-interacting [Formula: see text]CDM framework.
We will introduce new Special Conformal Killing vector fields for geometrodynamics. For Abelian and Yang-Mills theories. We will take advantage of the remarkable properties of the new tetrads introduced previously in order to construct these new Killing vector fields.
The observed late-time cosmic positive acceleration remains unexplained within the standard general relativity unless one assumes an unnaturally fine-tuned cosmological constant/dark energy. We propose an alternative mechanism in which positively accelerated expansion arises from an exponential correction to the entropy-area relation, leading to modified Friedmann equations without invoking a cosmological constant/dark energy. Starting from the thermodynamic formulation at the cosmological apparent horizon, we derive the background dynamics, including the Hubble rate, distance measures, lookback time, and then confront the model predictions with Type Ia supernova data along with recent data released from Planck/DESI collaborations. Using parameter values calibrated with Planck 2018 results and DESI DR1 and DR2 wCDM constrains, we show that a small negative entropy correction reproduces the expected matter-dominated behavior at higher redshifts, while naturally driving late-time positive acceleration of the cosmic expansion at smaller redshifts. The resulting distance modulus agrees well with observations, and diagnostic test Om(z) indicates a mild quintessence-like behavior. A stability analysis identifies a narrow range of viable parameter values consistent with current measurements of H 0 and dark energy equation of state. These results demonstrate that an exponential entropy correction is capable of providig an observationally consistent and theoretically well-motivated explanation of the late time cosmic speedup without adopting a cosmological constant/dark energy, suggesting promising avenues for full-likelihood parameter estimation and structure formation studies.
We investigate the thermodynamic behavior of galaxy clusters by employing statistical mechanical techniques. The canonical partition function is derived under this modified potential, from which key thermodynamic quantities including entropy, enthalpy, specific heat, and chemical potential are deduced. We make a comparison of the distribution function developed under the relativistically corrected gravitational potential with the distribution pattern deduced from data obtained via Data Release 10, 12 (DR10, 12) of Sloan Digital Sky Survey (SDSS).
This paper investigates a cosmological model based on a non-minimally coupled Yang-Mills field in the framework of a spatially flat FLRWuniverse. The model includes general functions describing the coupling between the Yang-Mills field and gravity, as well as its self-interaction potential. To further analyze the model, the Noether symmetry approach is used as a systematic method to identify conserved quantities and reduce the complexity of the dynamical system. By imposing the existence of a Noether symmetry, the initially arbitrary coupling functions are constrained, and the exact cosmological solutions compatible with observational data are found. It is shown that, under suitable conditions, Yang-Mills field behaves as a dark-energy component capable of driving the accelerated expansion of the universe.
This work explores the trajectories of test particles moving around a charged Black Hole subject to quantum corrections. The gravitational background follows a Reissner–Nordström configuration embedded in a Kiselev spacetime. Using the effective potential formalism, circular orbits in equatorial plane are analyzed. Analytical form of conserved energy and angular momentum are derived. The study identifies the location of innermost stable circular orbits and investigates the effective force. Additionally oscillations near the equatorial plane are examined to compute the radial, vertical and orbital frequencies as well as the periastron precession frequency. The overall results show that the model parameter significantly affect the evolution of test particle motion with in the gravitational field. In addition to the dynamical analysis, the thermodynamics behavior of the Black Hole is also examined. We study the profile of mass, temperature, specific heat and energy emission. This helps us how the model parameters affect thermal stability and radiation. Overall, the model remains thermodynamically consistent.
The [Formula: see text] theory of gravity, formulated in terms of the invariants [Formula: see text] and [Formula: see text] associated with the determinants of the Ricci and energy-momentum tensors, is examined. In this framework, which couples geometry to matter in a nontrivial manner, both the Ricci and energy-momentum tensors are assumed to be invertible, and the field equations are derived by extremizing the action with respect to the space-time metric and the independent Palatini connection. The theory naturally gives rise to an intrinsic bimetric structure through a disformal transformation governed jointly by curvature and matter. This structure leads to the non-conservation of energy and momentum, as well as to non-geodesic motion driven by an emergent force expressed in terms of [Formula: see text] and [Formula: see text], thereby extending the dynamics well beyond those of conventional gravitational models. A perfect fluid, serving as a cosmological model with an invertible energy-momentum tensor, provides a suitable matter sector for the model, enabling a detailed characterization of the geometry-matter interplay in terms of the pressure and density. We then extend our investigation to the barotropic equation of state and to the Ricci tensor, the latter being a conformal transformation of the geometric metric dictated by the deformation function [Formula: see text]. Our analysis shows that the theory dynamically induces an effective cosmological constant [Formula: see text] that depends on the state parameters, thereby providing a geometric mechanism capable of generating late-time cosmic acceleration.
We study whether the so-called Starobinsky-Grisaru-Zanon (SGZ) gravity, which is a novel fourth-order gravity model involving the so-called Grisaru-Zanon term, admits a stable de Sitter solution. First, we derive the corresponding field equations of the SGZ gravity for the spatially flat Friedmann-Lemaitre-Robertson-Walker metric by using an effective method based on the Euler-Lagrange equations. Then, we figure out an exact de Sitter solution of these field equations for the first time. Finally, we point out, through the dynamical system method, that the obtained de Sitter solution is always unstable. Interestingly, although the Starobinsky R-2 term does not contribute to the value of the obtained de Sitter solution, it does affect the instability of this solution.
In this paper, we clarify a key point in the geometric reinterpretation of the Grosse-Wulkenhaar (GW) model proposed in "Geometry of the Grosse-Wulkenhaar model" [J. High Energy Phys. 3 (2010) 53]. Specifically, we show that the analysis in Sec. 6 of that paper was performed not for the actual Omega-term in the GW action, which involves both ordinary and star-products, but for a closely related term containing only star-products. Once corrected, the main conclusion - relating the harmonic potential term to background curvature - remains valid, though the parameter identification must be revised. This also resolves a discrepancy concerning the emergence of certain vacuum solutions in the self-dual limit of the model.
In this work, we develop a relativistic description of the isotropic, charged pulsar CenX-3 by embedding it in the f(R,T) gravity framework-a modification of Einsteins general relativity (GR) in which the action depends on both the Ricci scalar R and the trace of the energy-momentum tensor T. Beginning with the well-behaved Durgapal-V metric functions, we derive a spherically symmetric interior solution to the coupled Einstein-Maxwell field equations modified by the f(R,T) term. To fix the model parameters, we match the observed mass M = 1.49 +/- 0.08 M-circle dot and radius R = 9.178(-0.130)(+0.130) km of CenX-3, enforcing continuity at the stellar surface with the exterior Reissner Nordstrom metric. Our analysis confirms that the solution satisfies all physical acceptability requirements including the energy conditions, causality constraints, and stability criteria throughout the configuration. The incorporation of electric charge and matter-geometry coupling in f(R,T) gravity thus offers a robust extension of GR, capable of producing consistent models for compact stellar objects.
In this paper, we investigated the existence of non-Einstein homogeneous critical metrics on homogeneous pseudo-Riemannian four-manifolds with nontrivial isotropy. Specifically, we focused on the presence of these metrics within four-dimensional non-reductive homogeneous manifolds. Our study aims to shed light on the underlying geometric structures and contribute to a deeper understanding of these mathematical constructs.
We investigate the viability of modified teleparallel f(T,& Tscr; ) gravity through a systematic analysis of energy conditions in a spatially flat FLRW universe. Two representative models are considered: a linear form f(T,& Tscr; ) = alpha T + beta & Tscr; and a nonlinear square-root form f(T,& Tscr; ) = alpha-T + beta & Tscr;. Using current observational values of the Hubble and deceleration parameters, we derive explicit constraints on the null (NEC), weak (WEC), dominant (DEC), and strong (SEC) energy conditions. The results show that NEC, WEC, and DEC are satisfied within well-defined regions of the parameter space, while SEC is consistently violated, providing a natural explanation for late-time cosmic acceleration. The corresponding equation of state parameter remains in the range - 1 < omega < -1 3, indicating a quintessence-like behavior compatible with observational constraints. A key result of this work is that, in the square-root model, the energy conditions become independent of the torsion coupling parameter alpha, revealing a non-trivial decoupling between geometric corrections and matter contributions. These findings suggest that f(T,& Tscr; ) gravity offers a consistent framework for explaining accelerated cosmic expansion, while providing clear constraints on model parameters from fundamental physical conditions.
We investigate the evolution of black hole mass for a Finslerian Kiselev black hole embedded in a cosmological background under various dark energy equation of state parametrizations, including Linear, Chevallier-Polarski-Linder (CPL), Jassal-Bagla-Padmanabhan (JBP) and Logarithmic models. The logarithmic mass ratio log10[M(z)/M0] is found to be highly sensitive to the redshift-dependent evolution of the dynamical dark energy equation of state parameter omega(z), with gentle slopes in Linear, Logarithmic and CPL models indicating quasi-static accretion and steep slopes in JBP corresponding to rapid late time variations highlighting transient suppression or enhancement of accretion due to repulsive dark energy effects. The peaks, minima and amplitude variations in the mass ratio arise from the combined effects of horizon thermodynamics, the changing pressure of the quintessence-like fluid and cosmic expansion. These features show that the mass evolution of the Finslerian Kiselev black hole is governed by dark energy dynamics and the effective gravitational influence of the surrounding cosmic fluid. Our results demonstrate that black hole accretion acts as a sensitive probe of the time-dependent cosmic pressure landscape and provides physical insights into the coupling between local strong gravity and global accelerated expansion.
In this survey, we study equilibrium thermodynamics through the lens of contact geometry. On the Gibbs space with contact one-form Theta = dE - TdS + PdV, equilibrium states constitute a 2-dimensional Legendre submanifold L subset of & Ropf;(5) characterized by Theta|(L) = 0. In particular, in this paper, we study the connection between the Legendre submanifolds associated to different thermodynamic potentials and Maxwell relations. Using exterior calculus, we show that Maxwell relations are precisely the integrability conditions d Theta|(L) = 0 and the pullback of two-form vanishes on the Legendre submanifold L. We describe Weinhold or Ruppeiner metric on the thermodynamic phase space associated to thermodynamic potentials. We also give a brief account of the Callen-Tisza treatment. We explore contact Hamiltonian mechanics and symplectic mechanics using the map between contactomorphism and symplectomorphism. The symplectization of thermodynamics is given via the map between contact form and Liouville form. This unifies Maxwell integrability, Legendre invariance of potentials and metric stability within a single contact-symplectic framework.
This paper constructs an anisotropic stellar model for static spherically symmetric geometries in & Fouriertrf;(& Qscr;) gravity. Corresponding to a linear form & Fouriertrf;(& Qscr;) = gamma(1)& Qscr; + gamma(2), we derive the modified gravitational field equations. For a specific case, we assume the Tolman metric potential together with the modified Chaplygin gas equation of state and derive an exact solution. Considering the structure and dynamical behavior of the stars, we apply this model to a particular compact star, EXO 1785-248, by processing a Schwarzschild exterior along with a static spherical interior. We analyze effective matter variables, energy conditions, redshift profiles and parameters of the equation of state for H-1 = 0.25, H-1 = 0.30 and five different values of & Fouriertrf;(& Qscr;) constant gamma(1). Then we present a comparison between the classical case and & Fouriertrf;(& Qscr;) gravity with respect to the known stability and viability tests. The & Fouriertrf;(& Qscr;) model meets all the requirements for realistic stellar structures, and this is in contrast with General Relativity (GR), which does not satisfy the conditions for the same configuration. The aforementioned findings illustrate the potential and ability of & Fouriertrf;(& Qscr;) gravity to serve as a legitimate theory to explain the anisotropic compact stars that are based on a modified Chaplygin gas equation of state.
