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In this paper, we investigate in this paper the Type IV singular bouncing in the framework of f (R ,) theory of gravity where R and mean the curvature scalar and the Gauss–Bonnet invariant, respectively. Cosmological f (R ,) models constrained by the slow-roll evolution is reconstructed and their explicit forms are provided near the bounce and far away from it. One obtains finally two models whose stability is numerically analyzed in this work. Our results show that the stability of the reconstructed models is very affected by their parameters. The model far from the singularity recovers stability quickly than the model near the singularity. [ABSTRACT FROM AUTHOR]

The primary objective of this paper is to examine singularity-free solutions within the framework of anisotropic solutions for the Chaplygin equation of state in f (R , ϕ , X) modified gravity theory. Herein, R signifies the Ricci scalar, ϕ denotes the scalar field, and X represents the kinetic term associated with ϕ. The investigation employs the Krori–Barua metric to explore the characteristics of an anisotropic compact star. In the course of our analysis, we specifically consider observational data about three distinct stellar structures: Her X-I, LMC X-4, and 4U 1538-52. Our inquiry extends to the graphical examination of various physical parameters, encompassing energy density, pressure components, anisotropic components, equation of state parameters, equilibrium conditions, stability analysis, adiabatic index, and energy conditions. Furthermore, we delve into the intricacies of the mass-radius function, compactness factor, and surface redshift–integral features of charged compact stars. The culmination of our findings suggests that the f (R , ϕ , X) theory of gravity when subjected to observational scrutiny, manifests as realistic, stable, and devoid of singularities. [ABSTRACT FROM AUTHOR]

In this paper, we review a recently offered notion of quasi-static evolution of the axial self-gravitating structures at large scales and the criterium to characterize the corresponding evolutionary aspects under the influence of strong curvature regimes. In doing so, we examine the axial source's dynamic and quasi-static behavior within the parameters of various modified gravity theories. We address the formalism of these notions and their possible implications in studying the dissipative and anisotropic configuration. We initiate by considering higher-order curvature gravity. The Palatini formalism of f (R) gravity is also taken into consideration to analyze the behavior of the kinematical as well as the dynamical variables of the proposed problem. The set of invariant velocities is defined to comprehend the concept of quasi-static approximation that enhances the stability of the system in contrast to the dynamic mode. It is identified that vorticity and distinct versions of the structure scalars Y I , Y II and Y KL play an important role in revealing the significant effects of a fluid's anisotropy. As another example of evolution, we check the influence of Palatini-based factors on the shearing motion of the object. A comparison-based study of the physical nature of distinct curvature factors on the propagation of the axial source is exhibited. This provides the intriguing platform to grasp the notion of quasi-static evolution together with the distinct curvature factors at current time scenario. The importance of slowly evolving axially symmetric regimes will be addressed through the distinct modified gravitational context. Finally, we share a list of queries that, we believe, deserve to be addressed in the near future. [ABSTRACT FROM AUTHOR]

In this paper, we propose a specialized parameterization for the Hubble parameter, inspired by Λ CDM cosmology, to investigate the cosmic expansion history of the Universe. This parameterization is employed to analyze the universe's late-time behavior within the context of Q n gravity, where Q represents non-metricity. By using data from 57 Hubble data points, 1048 supernova (SNe) data points, and six Baryon Acoustic Oscillation (BAO) data points, we determine the optimal values for the model parameters. Additionally, we explore three distinct cosmological models based on the parameter n , specifically when it takes on the values of 0. 5 5 , 1. 5 and 2. 0. The results of our analysis indicate that our proposed parameterization, along with the associated models for different values of n , predicts an accelerated cosmic expansion phase. [ABSTRACT FROM AUTHOR]

In this paper, the coupled system nonlinear (2 + 1)-dim Broer–Kaup–Kupershmit (BKK) equation under consideration is based on extension of modified rational expansion method. The various kinds of multiple soliton solutions named anti-kink soliton, traveling wave solutions, periodic solution, dark soliton, kink soliton, bright soliton, anti-kink bright solitons, kink bright solitons for nonlinear BKK system are successfully constructed under symbolic computation Mathematica. The calculated results are very interesting, different and novel which have not been investigated in past literature. The graphical demonstration of constructed solutions show by contour, 2D and 3D shape by using computer software Mathematica. The constructed multiple soliton solutions prove that EMRE approach is very straightforward, efficient, reliable and powerful for the investigation of other nonlinear partial differential equations. The investigated results will be described and play a keen role in the study of nonlinear physical phenomena in the area of physics and engineering. [ABSTRACT FROM AUTHOR]

General theory of relativity can be equivalently formulated on a flat spacetime associating a torsion-free affine connection of non-vanishing non-metricity scalar Q. In this paper, we present an extension of this, viz., the f (Q) theory of gravity, and explore the early evolution of the universe in the background of anisotropic Bianchi-I model. The f (Q) theory in the current setting through its geometric modification is quite successful in explaining the late time accelerated expansion. Here, we note that it accommodates latest released constraints on the inflationary parameters by Planck's collaboration group with excellent precession, but fails to produce a viable decelerated expansion in the radiation dominated era. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and characterize a pseudo-generalized Ricci-recurrent spacetimes and produce an example to verify the existence of such a spacetime. Then we demonstrate that a conformally flat generalized Ricci-recurrent spacetime with certain condition is a pseudo quasi-Einstein spacetime. Besides, it is proved that a pseudo-generalized Ricci-recurrent generalized Robertson–Walker spacetime represents a perfect fluid spacetime. Lastly, we study the impact of this spacetime under f (ℛ , T 2) and f (ℛ ∗) gravity scenario and deduce several energy conditions. [ABSTRACT FROM AUTHOR]

This paper is devoted to observe the physical attributes of isotropic relativistic spherical objects in the context of Rastall theory of gravity. In order to inspect the structural composition of spherical objects, the Tolman IV solution is taken into account. The unknown parameters associated with Tolman IV solution are evaluated through matching conditions with derived values of radii and masses of some specific star models. The consistency of the adopted ansatz is analyzed via graphical interpretation of matter variables, equation of state parameter, mass components, energy constraints, causality condition and stellar equation for several choices of Rastall parameter. It is observed that the considered solution does not admit singularities in the matter variables. Moreover, in accordance with the graphical analysis, the stellar models satisfy all physical requirements anticipated in a realistic star. It is also shown that for vanishing Rastall coupling parameter, the standard outcomes of general relativity can be retrieved. [ABSTRACT FROM AUTHOR]

In this paper, we explore the existence of wormholes in the context of f (R , T) gravity. The f (R , T) theory is a curvature-matter coupled modified gravity that depends on an arbitrary function of the Ricci scalar R and the trace of the stress-energy tensor T. In this work, we adopt two different choices for the matter Lagrangian density ( ℒ m = and ℒ m = p r ) and investigate the impact of each one on wormhole structure. By adequately specifying the redshift function and the shape function, we found a variety of exact wormhole solutions in the theory. Our finding indicates that for both classes of wormholes, the energy density is always positive throughout the spacetime, while the radial pressure is negative. This means exotic matter is necessary for the existence of wormholes in f (R , T) gravity. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to obtain physically stable stellar models coupled with anisotropic matter distribution in the context of f (ℛ , T 2) theory. For this, we consider a static spherical geometry and formulate modified field equations containing various unknowns such as matter determinants and metric potentials. We then obtain a unique solution to these equations by employing Durgapal–Fuloria ansatz possessing a constant doublet. We also use matching criteria to calculate the values of these constants by considering the Schwarzschild exterior spacetime. Two different viable models of this modified theory are adopted to analyze the behavior of effective matter variables, anisotropy, energy conditions, compactness and redshift in the interiors of Her X-1, PSR J0348-0432, LMC X-4, SMC X-1, Cen X-3, and SAX J 1808.4-3658 star candidates. We also check the stability of these models by using three different physical tests. It is concluded that our considered stars satisfy all the physical requirements and are stable in this modified gravity for the considered parametric values. [ABSTRACT FROM AUTHOR]

The observational evidence of f (R , , T) gravity in the FRW universe is the focus of the study. We provide a novel cosmological theory in this paper that was created within the f (R , , T) framework. We used the Markov Chain Monte Carlo (MCMC) method to limit the model parameters using the 31 Cosmic Chronometer points and 1048 Pantheon data points. We can efficiently explore the parameter space using this method. In order to compare our proposed f (R , , T) model to the well-known Λ CDM model, we take into account a parameterization of the Hubble parameter for solving the modified field equation. By studying these factors in the context of our new model, we get essential knowledge into the dynamics and evolution of the cosmos. State finder and Om Diagnostic, among other diagnostic tests, have been used to further analyze the behavior and consistency of our f (R , , T) model. These tests give us a greater understanding of our model's properties and their applicability to observational data. [ABSTRACT FROM AUTHOR]

In this paper, we construct the exact interior solutions for compact stellar objects for perfect fluid distribution in phantom region in the framework of a non-conserved theory, i.e. Rastall gravity (RG). Under these circumstances, we develop the Einstein field equations (EFEs) for spherically symmetric metric using general forms of metric potentials, a (r) = B r α + C r β and b (r) = A r γ , here α , β , γ ≥ 2 and α ≠ β. By matching of interior and exterior regions of the metric, we obtain the values of unknown constants of our considering model which helps to sketch the nature of important physical quantities like density, pressure, energy conditions, and stability. Finally, our obtained results lead us to conclude that our solutions are well behaved and physically viable for the specific choices of model parameters for two different stars (Vela X-1 and 4U1820-30). [ABSTRACT FROM AUTHOR]

This paper is devoted to study FRW universe in the context of Chern–Simons corrected f (R) gravity. In particular, the work provides the investigation of cosmological dynamics within modified gravity by assuming a suitable Hubble parameter that might result in a realistic bouncing universe. For this purpose, we consider a suitable Hubble parameter and examine the bouncing cosmology by assuming a well-known f (R) gravity model. Further, we explore the behavior of energy density and pressure profiles by employing the chosen Hubble parameter. We obtain positive and increasing trends of energy density during the bouncing phase while the negative behavior of pressure in our work could potentially be associated with cosmic expansion. We have also studied the energy conditions and in our case NEC is not violated perhaps due to the reason that the equation of state parameter is not crossing the phantom divide. However, the SEC is violated justifying a successful bounce. Moreover, the validation of DEC and TEC suggests that the chosen model is well behaved in nature. The Hubble parameter passing through the bouncing point shows an increasing trend, indicating an expansion phase after the bounce. The equation of state parameter is negative after the bouncing spot, particularly around ω ≈ − 1. This behavior justifies the current cosmic expansion. The deceleration parameter exhibits a negative behavior implies that the cosmological model demonstrates cosmic expansion. Thus all the results validate the existence of a bouncing universe with the chosen model in Chern–Simons corrected f (R) gravity. [ABSTRACT FROM AUTHOR]

The aim of this paper is to examine the singularity-free solutions for anisotropic stellar structures in f (R , ϕ) theory of gravity, where R denotes the Ricci scalar and ϕ represents the scalar field. For this purpose, we consider the spherically symmetric spacetime to discuss the stellar structures with anisotropic fluid. Moreover, the Einstein field equations are solved by using Chaplygin equation of state, and the Karori–Barua metric. To analyze the charged stellar structure, we use the matching conditions of spherically symmetric spacetime with the Reissner–Nordstrom exterior metric and develop some expressions for finding the unknown parameters. We further investigate the graphical behavior of energy density, pressure components, anisotropic component, equation of state parameters, equilibrium condition, stability analysis, adiabatic index and energy conditions. Conclusively, our considered stellar structures under observations are realistic, stable, and are free from any singularities. [ABSTRACT FROM AUTHOR]

Galactic rotation curve is a powerful indicator of the state of the gravitational field within a galaxy. The flatness of these curves indicates the presence of dark matter (DM) in galaxies and their clusters. In this paper, we focus on the possibility of explaining the rotation curves of spiral galaxies without postulating the existence of DM in the framework of f (ℛ , T) gravity, where the gravitational Lagrangian is written by an arbitrary function of ℛ , the Ricci scalar and of T , the trace of energy–momentum tensor T μ ν . We derive the gravitational field equations in this gravity theory for the static spherically symmetric spacetime and solve the equations for metric coefficients using a specific model that has minimal coupling between matter and geometry. The orbital motion of a massive test particle moving in a stable circular orbit is considered and the behavior of its tangential velocity with the help of the considered model is studied. We compare the theoretical result predicted by the model with observations of a sample of 19 galaxies by generating and fitting rotation curves for the test particle to check the viability of the model. It is observed that the model could almost successfully explain the galactic dynamics of these galaxies without the need of DM at large distances from the galactic center. [ABSTRACT FROM AUTHOR]

The construction of compact star models with quintessence and cloud of strings anisotropic fluid lays the foundation for the research presented in this paper, which focuses on the ansatz of f(Q) gravity. We utilized a spherically symmetric spacetime to derive the field equations incorporating quintessence and cloud of strings anisotropic matter fields. The well-known Karmarkar condition was employed to obtain the gravitational components of the spherically symmetric spacetime. The constant parameters used in the study were obtained by applying junction conditions on the interior and exterior spacetimes. We used the mass and radius of P S R J 1 6 1 4 − 2 2 3 0 & S M C X − 1 , which are already present in the literature. Afterward, we calculated the important properties of quintessence stars in the presence of cloud of strings to ensure the stability and physical presence of compact models. To achieve this goal, we studied features such as energy density, quintessence density, pressure profiles, gradients, anisotropic factor, energy conditions, sound speeds, TOV forces, EoS components, mass function, compactification and redshift. [ABSTRACT FROM AUTHOR]

In this paper, the basic Einstein–Hilbert cosmological model is extended by adding a new functional F (G , T μ ν T μ ν) in the fundamental action, encoding specific geometrical effects due to a nontrivial coupling with the Gauss–Bonnet invariant (G), and the energy–momentum squared term ( T μ ν T μ ν ). After obtaining the corresponding gravitational field equations for the specific decomposition where F (G , T μ ν T μ ν) = f (G) + g (T μ ν T μ ν) , we have explored the physical features of the cosmological model by considering the linear stability theory, an important analytical tool in the cosmological theory which can reveal the dynamical characteristics of the phase space. The analytical exploration of the corresponding phase space structure revealed that the present model can represent a viable dark energy model, with various stationary points where the effective equation of state corresponds to a de-Sitter epoch, possible explaining the early and late time acceleration of the Universe. [ABSTRACT FROM AUTHOR]

This paper explores the dynamic behavior of the universe within the framework of the f (R , G) theory of gravity. Here, R and G represent the Ricci scalar and Gauss–Bonnet invariant, respectively. By solving the modified field equations with the chosen f (R , G) function, specifically f (R , G) = R + m R 2 + n G 2 , we determine the best fit values of model parameters that are consistent with recent observational datasets. These datasets include 57 data points from the Cosmic Chronometers, Pantheon, and BAO datasets. Furthermore, we analyze the physical properties of cosmographic parameters, such as energy density and pressure, corresponding to the constrained values of the model parameters. The evolution of the deceleration parameter in our study indicates a transition from a decelerated phase to an accelerated phase in the universe. Remarkably, our f (R , G) cosmological model effectively describes the late-time cosmic acceleration without requiring the introduction of a dark energy component in the field equations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the framework of the newly proposed modified theory of gravity named f (R , A) gravity, wherein R and A signify the Ricci and anticurvature scalars, respectively. For our cosmic discussions, we evaluate a renowned f (R , A) model, incorporating various forms of the scale factor within the context of Friedmann–Robertson–Walker (FRW) spacetime. Our exploration delves into energy conditions, the effective equation of state parameter and the stability of models within the f (R , A) theory. These models are further elucidated through graphical representations plotted against time and their respective model constants. Notably, it is observed that scale factors with exponential terms yield more consistent results in comparison to those of power-law forms, given specific values of model constants. [ABSTRACT FROM AUTHOR]

In this paper, we study an isotropic and homogeneous Friedmann–Lemaitre–Robertson–Walker cosmological model in Weyl type f (Q , T) gravity with a dynamic deceleration parameter. The solution of the field equations is found using a variable deceleration parameter, viz., q = n + m H , with q the deceleration parameter, n and m constants, and H the Hubble parameter [Tiwari et al., Eur. Phys. J. Plus 132, 1 (2017)]. Then we calculate the values of the model parameters that are most likely to accord with the most recent observational data sets. We make use of the 57 CC points, SN and BAO datasets. We have contracted a graphical representation of the dynamical behavior of the cosmological parameters (the Hubble parameter, the deceleration parameter, the energy density and the equation of state) in terms of the redshift. To investigate the various eras of the universe, the evolution of the statefinder trajectory pairs (s , r) and (q , r) are studied. It is shown that the main energy component of the model is ordinary matter, which behaves initially as the SCDM model and then later as a fluid resembling quintessence, which behaves as the well-known Λ CDM model. A suitable cosmological model is constructed after analyzing the physical parameters of the model, the O m (z) diagnostic analysis. [ABSTRACT FROM AUTHOR]

Recently, Rajagopal et al. presented an asymptotically AdS black hole metric whose thermodynamics qualitatively mimics the behavior of the Van der Waals fluid by treating the cosmological constant as a thermodynamic pressure. In some studies in the literature, authors have discussed the effects of deformed algebras such as generalized and extended uncertainty principles on the thermal quantities of these black holes. In this paper, we considered another deformation, the rainbow gravity formalism, and we investigated its impact on the Van der Waal black hole thermodynamics. To this end, we first generated the modified lapse and mass functions, and then we derived the modified thermal quantities such as thermodynamic volume, Hawking temperature, entropy, and specific heat functions. Finally, we explored the thermodynamics of a black hole, which mimics the thermodynamics of an ideal gas, under the influence of the rainbow gravity formalism. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop the isotropic and anisotropic quark stars configurations in the context of f (T ,) gravity in the static spherically symmetric background. To explore the combined effects of torsion scalar T and the trace of energy–momentum tensor (EMT) on relativistic astrophysics, we use diagonal as well as non-diagonal tetrad fields. By considering the conformal Killing vectors along with the MIT bag model, the interior solutions of the field equations corresponding to the linear f (T ,) = α T (r) + β (r) + ϕ model (in which α , β are the constants and ϕ indicates the cosmological constant) are calculated. The feasibility of the obtained solutions is confirmed by implementing several physical tests. The model parameters are constrained subject to the existence and stability of the quark star models. We formulate the energy constraints, stability equations, mass function, compactness and redshift factor, and present the graphical analysis of all physical quantities. It is found that the derived solutions for both diagonal and non-diagonal tetrad exhibit well-behaved profiles in the framework of modified teleparallel gravity. [ABSTRACT FROM AUTHOR]

In this paper, we refer to the early hypotheses on superconductivity in the models of the electron as an extended particle, and show how Nonlinear Electrodynamics minimally coupled to Gravity (NED-GR) predicts, without additional assumptions, the existence of primary superconductivity as the universal property of regular electrically charged rotating black holes and electromagnetic spinning solitons, replacing naked singularities and including that with the parameters of the electron. NED-GR dynamical equations describe basic generic properties of these objects in a self-consistent and the model-independent way, and establish the existence of the superconducting ring current in their deep interiors, which presents the non-dissipative source of the electromagnetic field of an object and provides its practically unlimited life time. [ABSTRACT FROM AUTHOR]

This paper investigates the static spherically symmetric vacuum solutions of Brans–Dicke Theory of Gravity. In this paper, we systematically derive the static spherically symmetric solutions by starting with the general static spherically symmetric anzats, discovering the nonzero Christoffel symbols, nonzero Ricci tensor components and the Ricci Scalar. These results allow us to rewrite the four Brans–Dicke gravitational field equations explicitly in terms of the metric components, the scalar field and its scalar potential. This paper systematically explains and shows how to modify these linear second-order ordinary differential equations in order to be able to find the solution of the scalar field, the metric components and the scalar potential analytically. We successfully find the most general solution of the static spherically symmetric vacuum solutions of Brans–Dicke gravity and the well-known Schwarzschild solution is recovered as the simplest solution. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the precise computation of anisotropic extensions for the Tolman IV solution. These extensions are achieved through the utilization of the extended gravitational decoupling scheme within the framework of f (R , T 2) gravity, where R is the Ricci scalar and T 2 is the contraction of energy–momentum tensor. In this context, we select a linear model characterized by the expression f (R , T 2) = R + ξ T 2 , where the parameter ξ establishes a connection between the geometric and matter components. The extended gravitational decoupling technique incorporates a decoupling parameter that governs the extent of the induced anisotropy. Deformations in the radial and temporal metric components lead to the decomposition of the field equations into two distinct subsystems. One of these sets pertains to the isotropic solution, while the other is addressed by implementing the extra constraints. We examine the outcomes through graphical analysis and investigate the viability and stability of the obtained anisotropic solutions for the celestial object. Moreover, we study the mass, compactness and surface redshift of the system to gain a comprehensive understanding of its characteristics. It is concluded that this technique in this modified gravity yields physically acceptable solutions. [ABSTRACT FROM AUTHOR]

In this paper, we explore the physical properties and characteristics of static, spherically symmetric wormholes in the background of Rastall–Rainbow gravity. The Rastall–Rainbow gravity theory has recently been proposed as a combination of two theories, namely, the Rastall theory and the Rainbow description. We implemented noncommutativity by adopting two different distributions of energy density (Gaussian and Lorentzian) in the Morris and Thorne metric. We solve the field equations analytically and discuss all the properties of wormholes depending on the two model parameters. Notably, for specific parameter ranges, one can alleviate the violation of the WEC at the throat and its neighborhood. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the behavior of a scalar bosonic field within the backdrop of Eddington-inspired Born–Infeld gravity with a global monopole configuration. Additionally, we consider the presence of both scalar and vector potentials. To introduce the scalar potential, we perform a transformation on the mass term, replacing M 2 with (M + S) 2 . For the vector potential, we apply a minimal coupling scheme, transforming p μ → D μ ≡ (p μ − e A μ) within the relativistic Klein–Gordon equation. We opt for a harmonic oscillator scenario where the scalar and vector potentials are equal, i.e. S = V ∝ x 2 . Through this setup, we analytically solve the wave equation using the confluent Heun equation form. Subsequently, we delve into the quantum system in the absence of any potential, determining the permissible values for bound-state relativistic energy levels and the scalar field's wave function. Our analysis reveals that the energy levels and wave function are influenced by various parameters present in the eigenvalue expression. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop the isotropic and anisotropic quark stars configurations in the context of f (T ,) gravity in the static spherically symmetric background. To explore the combined effects of torsion scalar T and the trace of energy–momentum tensor (EMT) on relativistic astrophysics, we use diagonal as well as non-diagonal tetrad fields. By considering the conformal Killing vectors along with the MIT bag model, the interior solutions of the field equations corresponding to the linear f (T ,) = α T (r) + β (r) + ϕ model (in which α , β are the constants and ϕ indicates the cosmological constant) are calculated. The feasibility of the obtained solutions is confirmed by implementing several physical tests. The model parameters are constrained subject to the existence and stability of the quark star models. We formulate the energy constraints, stability equations, mass function, compactness and redshift factor, and present the graphical analysis of all physical quantities. It is found that the derived solutions for both diagonal and non-diagonal tetrad exhibit well-behaved profiles in the framework of modified teleparallel gravity. [ABSTRACT FROM AUTHOR]

General relativity has been the dominant paradigm theory of gravity for the last century, it manages to explain a plethora of astronomical and cosmological observations with high accuracy. A major challenge faced by general relativity is, that it predicts a singularity as the beginning of our universe. In this paper, we shall explore a well-known idea in the literature that of the emergent universe and its viability according to Planck 2018 data and BBN constraints. [ABSTRACT FROM AUTHOR]

In this paper, our principal objective is to investigate the impact of disclination and throat radius of a three-dimensional traversable wormhole on quantum oscillator fields. Specifically, we focus on Perry–Mann-type wormhole with disclination while also considering the influence of rainbow gravity's. We derive the radial equation of the relativistic Klein–Gordon oscillator within this wormhole background under the effects of gravity's rainbow and the analytical eigenvalue solution is obtained using the confluent Heun function. In fact, we show that the behavior of the oscillator fields is significantly influenced not only by the presence of disclination and the throat radius but also by the parameter of rainbow gravity's. We choose various such rainbow functions to present and analyze the eigenvalue solutions of the quantum oscillator fields. [ABSTRACT FROM AUTHOR]

In this paper, we study the Chaplygin gas equation in curvature-matter coupling gravity to describe the observed expansion of the universe. We consider the Chaplygin gas equation of state in terms of the energy density ρ and pressure p , by the relationship p = − A ρ and the curvature-matter coupling gravity as f (R , T) , where A is a positive constant, R and T denote, respectively, the Ricci scalar and the trace of energy–momentum tensor. Considering the gravitational lagrangian in the form f (R , T) = R + h (T) , where we used two forms of h (T) and by assuming a perfect fluid as matter source, we determined through the modified Friedmann equations, the corresponding energy and pressure for each model. By using the free parameters of our models, we performed the numerical results of the energy conditions to study its viability. Furthermore, we have derived some cosmological parameters like deceleration parameter and statefinder parameters and graphically investigated the nature of these parameters in Chaplygin gas model. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the dynamical behavior of the universe with a flat FLRW model in f (R , G) gravity, where R and G both signify the Ricci scalar and Gauss–Bonnet invariant. Furthermore, in order to determine the model's behavior, it must have the late-time universe's behavior, which involves both an accelerated expansion as well as ending in a big rip. We present a model that begins with a point-type singularity, i.e. a point with zero volume and infinite energy density, by using parametrization of the scale factor a (t). The model's actions are accelerating and expanding at the moment, and Λ CDM in late times. Our extensive analysis encompasses the energy conditions, dynamics of certain model solutions and additional cosmological tests through a dominant model. Finally, the proposed framework acts exactly like a quintessence dark energy model in the current time and is reliable with standard cosmology Λ CDM in late times. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the feasibility and the appearance of charged thin-shell wormholes using generalized Chaplygin gas under the influence of minimally coupled f (R , T) gravitational theory. Here, f is a generic function of the scalar curvature R and the trace of stress-energy tensor T. We explore different components of Lanczos equations in the context of a specific f (R , T) functional form, i.e. f (R , T) = R + 2 λ T , by applying junction conditions on field equations. We study static stable solutions using radial perturbation and the generalized Chaplygin gas equation of state (EoS) with the isotropic environment. We investigate the stable (unstable) static wormhole solutions for various physical parametric values and illustrate them graphically. [ABSTRACT FROM AUTHOR]

In this paper, we consider a charged BTZ black hole in asymptotically AdS spacetime of massive gravity to study the effect of the thermal fluctuations on the black hole thermodynamics. We consider the Einstein–Born–Infeld solution and investigate critical points and stability. We also compare the results with the case of Einstein–Maxwell solutions. Besides, we find that thermal fluctuations, which appear as a logarithmic term in the entropy, affect the stability of the black hole and change the phase transition point. Moreover, we study the geometrical thermodynamics and find that the behavior of the linear Maxwell solution is the same as the nonlinear one. [ABSTRACT FROM AUTHOR]

It was shown recently that a very simple nonlocal de Sitter gravity model contains exact vacuum cosmological solution which mimics dark energy and dark matter in flat space. Some other interesting solutions have been also found. In this paper, we proceed with finding several new exact cosmological solutions which belong to Bianchi I space. These solutions are simple generalizations of solutions previously found in the FLRW case of the same nonlocal de Sitter gravity model. Obtained results are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we present an introduction to cosmic inflation in the framework of Palatini gravity, which provides an intriguing alternative to the conventional metric formulation of gravity. In the latter, only the metric specifies the spacetime geometry, whereas in the former, the metric and the spacetime connection are independent variables—an option that can result in a gravity theory distinct from the metric one. In scenarios where the field(s) responsible for cosmic inflation are non-minimally coupled to gravity or the gravitational sector is extended, assumptions about the underlying gravitational degrees of freedom can have substantial implications for the observational effects of inflation. We examine this explicitly by discussing various compelling scenarios, such as Higgs inflation with a non-minimal coupling to gravity, Higgs inflation with a non-minimal derivative coupling, ℛ 2 inflation, and beyond. We also comment on reheating in these models. Finally, as an application of the general results of Palatini ℛ 2 inflation, we review a model of successful quintessential inflation, where a single scalar field acts initially as the inflaton and then becomes dynamical dark energy, in agreement will all experimental constraints. [ABSTRACT FROM AUTHOR]

Second-order-derivative plus fourth-order-derivative gravity is the ultraviolet completion of second-order-derivative quantum Einstein gravity. While it achieves renormalizability through states of negative Dirac norm, the unitarity violation that this would entail can be postponed to Planck energies. As we show in this paper, the theory has a different problem, one that occurs at all energy scales, namely that the Dirac norm of the vacuum of the theory is not finite. To establish this, we present a procedure for determining the norm of the vacuum in any quantum field theory. With the Dirac norm of the vacuum of the second-order-derivative plus fourth-order-derivative theory not being finite, the Feynman rules that are used to establish renormalizability are not valid, as is the assumption that the theory can be used as an effective theory at energies well below the Planck scale. This lack of finiteness is also manifested in the fact that the Lorentzian path integral for the theory is divergent. Because the vacuum Dirac norm is not finite, the Hamiltonian of the theory is not Hermitian. However, it turns out to be P T symmetric. When one continues the theory into the complex plane and uses the P T symmetry inner product, viz. the overlap of the left-eigenstate of the Hamiltonian with its right-eigenstate, one then finds that for the vacuum this norm is both finite and positive, the Feynman rules now are valid, the Lorentzian path integral now is well behaved, and the theory now can serve as a low energy effective theory, one that we show to have a real classical gravity limit. Consequently, the theory can now be offered as a fully consistent, unitary and renormalizable theory of quantum gravity. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the localization of five-dimensional tensor gauge fields called Kalb–Ramond fields in the modified teleparallel braneworld models. The aforementioned branes are generated by gravity coupled to a real scalar field with nonstandard kinetic terms. For two specific forms of the noncanonical expressions, background scalar field solutions are particularly discussed in the presence of different forms of f (T) gravity. By applying nonminimal coupling functions in the tensor gauge field action, it is shown that massless zero modes of Kalb–Ramond gauge fields can be localized on the f (T) branes with noncanonical scalar fields. We also find that potentials of Kalb–Ramond massive modes are volcano-like regarding the equation of motion in the supersymmetric quantum mechanic scenario. Furthermore, the effects of parameters that control the deviation of the usual teleparallel theory are considered on the massless Kaluza–Klein mode and effective potential. [ABSTRACT FROM AUTHOR]

This paper accords with the theoretical study of lifting and drainage of Sisko fluid film on a vertically upward moving cylinder with surface tension. The flow on cylinder is induced by the upward motion of the cylinder, gravity and surface tension gradient. The resulting nonlinear ordinary differential equation is solved for a series form solution by making use of the Adomian decomposition method (ADM). Expressions for the flow variables like velocity, volume flow rate, shear stress and surface tension are derived. Positions of stationary points and thickness of uniform film are computed numerically in MATHEMATICA. The inverse capillary number C, Stokes number S t , Sisko fluid parameter β and fluid behavior index n emerged as flow control parameters. The study showed that the positions of stationary points relocate towards the surface of the cylinder by the increase of C and S t while their positions relocate towards the fluid–air interface with increasing β and n. Thickness of uniform film decreases when the values of C and S t are increased whilst it increases with the increase of β and n. Analogy between the Newtonian fluid and the Sisko fluid's shear thinning and shear thickening behaviors for positions of stationary points, thickness of uniform film and surface tension is also made. [ABSTRACT FROM AUTHOR]

Circa 1962 Hans A. Buchdahl pioneered a program — and made significant progress — seeking vacuo configurations in pure ℛ 2 gravity (H. A. Buchdahl, Nuovo Cimento 23 (1962) 141). Unfortunately, he deemed the final step in his calculations impassable and prematurely suspended his pursuit. Since then, his achievements on this front have faded into dormancy. Unbeknownst to Buchdahl himself, the ℛ 2 vacua that he sought were within his striking distance. In our recent three-paper body of work published in Nguyen (Phys. Rev. D 106 (2022) 104004; Phys. Rev. D 107 (2023) 104008; Phys. Rev. D 107 (2023) 104009), we broke this six-decades-old impasse and accomplished his goal: A novel class of metrics, describing non-Schwarzschild spacetimes in quadratic gravity and carrying a hallmark of higher-derivative characteristic. Intriguing properties of Buchdahl-inspired spacetimes and their associated Morris–Thorne–Buchdahl wormholes — summarized herein — embody a new branch of phenomenology that transcends the Einstein–Hilbert paradigm. May this unsung legacy of Hans A. Buchdahl long "forsaken" and "forgotten" finally live on Our essay is a passageway bridging the past and the future. The past is rooted in a research program originated but left unfinished by Buchdahl going back threescore years ago. The future is the new horizons his program brings forth. In between is our labor — summarized in a three-installment "Beyond Schwarzschild–de Sitter spacetimes" series[1–3] — to advance the Buchdahl program and achieve his ultimate goal. [ABSTRACT FROM AUTHOR]

This paper proposes a new framework to investigate the spherically symmetric of anisotropic stars with clouds of strings and quintessence field in Rastall gravity. We develop the field equations in a spherically symmetric space–time with a quintessence field and clouds of string. We utilize the mass and radius of Her X-1, Vela X-1, SMC X-1, SAX J1808 0.4-3658 and 4 U 1538-52, which are well mentioned in the literature. We applied the matching conditions by considering outer space calculated in Rastall gravity to evaluate the constants parameters. To check the stability and physical presence of compact models, we computed the most important features of quintessence stars in the presence of a cloud of strings. We explored characteristics including energy density, quintessence density, radial pressure, tangential pressure gradients, anisotropic factor, energy conditions, sound speeds, TOV forces, EoS components, mass function, compactification and redshift. [ABSTRACT FROM AUTHOR]

To make a comparison of energy conditions in the theory of general relativity and in the modified theories, we have considered f (R) , f (R , T) and f (R , T , Q) theories (where R and T are the Ricci scalar and trace of the energy–momentum tensor, respectively, while Q = T a b R a b ) to test the validity of all the four energy conditions. These energy conditions had been derived to check the viability of cosmological as well as astrophysical models. In this paper, we consider the standard Friedmann–Robertson–Walker spacetime representing the homogeneous and isotropic universe, and investigate the available literature on testing energy conditions as well as calculate these conditions ourselves. In order to provide the comparative results, we test these conditions analytically as well as graphically and present how energy bounds in modified theories depend on the values of the involved parameters and its validity within certain limits. We discuss here, that which of the modified theories comply with certain energy conditions, and hence provide a supporting argument on the existence of modified theories. [ABSTRACT FROM AUTHOR]

In this paper, we would like to examine whether a novel Starobinsky–Bel–Robinson (SBR) gravity model admits stable exponential inflationary solutions with or without spatial anisotropies. As a result, we are able to derive an exact de Sitter inflationary to this SBR model. Furthermore, we observe that an exact Bianchi type I inflationary solution does not exist in the SBR model. However, we find that a modified SBR model, in which the sign of coefficient of R 2 term is flipped from positive to negative, can admit the corresponding Bianchi type I inflationary solution. Unfortunately, stability analysis using the dynamical system approach indicates that both of these inflationary solutions turn out to be unstable. Interestingly, we show that a stable de Sitter inflationary solution can be obtained in the modified SBR gravity. [ABSTRACT FROM AUTHOR]

This paper aims to conduct an extensive examination of hyperbolically symmetrical static fluid distributions, wherein a precise analysis of their physical characteristics is carried out in the background of modified f (G , T) gravity, where G and T stands for Gauss Bonnet invariant and energy-momentum trace, respectively. The outcomes reveal that the energy density exhibits negative value, thus implying that any utilization of such fluids necessitates extremely demanding circumstances where quantum effects would be significantly influential. Furthermore, it has been determined that these fluid distributions cannot take the vicinity surrounding their central point of symmetry and leave behind an empty vacuum cavity in its place. Additionally, an appropriate definition for mass function and the complexity factor is determined. Eventually, we exhibit a broad strategy for accomplishing particular solutions and showcase several instances of exact analytical solutions in the presence of f (G , T) correction terms. [ABSTRACT FROM AUTHOR]

The theory of Hybrid metric-Palatini gravity was proposed by Harko et al. [Metric-Palatini gravity unifying local constraints and late-time cosmic acceleration, Phys. Rev. D 85 (2012) 084016.] in 2012 which could explain both local and cosmological observations. In this paper, this theory has been taken into account to obtain static, spherical, and symmetric charged traversable wormhole solutions. The shape of the wormhole is determined in two different cases with the simplest form of scalar field potential. It is obtained that asymptotically flat wormholes are possible in each case. The energy conditions, namely, null, weak, and strong energy conditions are tested in each case and the results are compared. [ABSTRACT FROM AUTHOR]

There is a formulation of unimodular gravity (UG) in which the unimodular metric is obtained out of an unrestricted one as γ μ ν = | g | − 1 n g μ ν . This unrestricted metric is only defined up to a Weyl rescaling. Physical charges like ADM energy or horizon entropy, however, are not Weyl invariant in general. In this paper a Weyl invariant definition of some physical charges is given. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the thermodynamical phase transitions of the spherically symmetric AdS black hole in Horava–Lifshitz (HL) gravity for the detailed balance violation parameter 0 ≤ ϵ 2 ≤ 1. First, by calculating the HP temperature T HP , the minimum temperature T min and the Gibbs free energy G of the AdS black hole in different values of parameter ϵ , we find that the HP phase transition can occur at all pressures. Comparing the HP temperature T HP with the minimum temperature T min , we notice that the ratio of T HP / T min tends to 1 when d → ∞. Second, for the small–large black hole phase transition of the AdS black hole, we discover that the black hole heat capacity is divergent at the minimum temperature T min , the small–large black hole phase transition occurs at the same time. Furthermore, the black hole entropy also exists S HP when T = T HP , and S min when the black hole temperature has its minimum T min , we surprisingly find that the ratio of S HP / S min tends to e when the dimension d → ∞ , which provides a general relation between the Hawking–Page phase transition and the small–large black hole phase transition of the AdS black hole in the large dimension. All in all, the ratios of typical temperature and entropy of two kinds of phase transitions tend to natural constant in the large dimension limit, which may imply to understand the nature of two different phase transitions. [ABSTRACT FROM AUTHOR]

This paper examines the structure of a gravitational vacuum star (also known as gravastar) in the background of f (ℜ , 2) theory. This hypothetical object can be treated as a substitute of a black hole, with three regions: (i) the internal region, (ii) the intrinsic shell and (iii) the outer region. We examine these geometries using Finch–Skea metric for the radial metric component along with the particular f (ℜ , 2) model. We determine singularity-free solutions for both the inner as well as thin-shell domains. The smooth matching of the interior region with external Schwarzschild spacetime is obtained through Israel matching constraints. Finally, we study various characteristics of gravastar domains including the equation-of-state parameter, proper length, entropy, energy as well as surface redshift. It is found that the compact gravastar structure is a viable alternate to the black hole in the perspective of this gravity. [ABSTRACT FROM AUTHOR]

In this paper, the traces of conformal twisted signature operators and noncommutative residue for compact manifolds with boundary are considered, the classic gravity representation for manifolds with boundary associated with conformal twisted signature operators and Kastler–Kalau–Walze-type theorems is explored. [ABSTRACT FROM AUTHOR]

The primary goal of this paper is to examine spacetimes admitting semiconformal curvature tensor in f (ℛ) modify gravity. The semiconformal flatness of general spacetime and spacetime in f (ℛ) gravity with perfect fluid, has been analyzed. For this consideration, we generate the forms of isotropic pressure p and energy density σ. After that, a few energy conditions are taken into account. Finally, we study the divergence-free semiconformal curvature tensor in f (ℛ) gravity in presence of perfect fluid. We emphasize that for recurrent or bi-recurrent energy–momentum tensor, Ricci tensor of this spacetime is semi-symmetric and consequently, the resulting spacetimes either accomplish inflation or possess fixed isotropic pressure and energy density. [ABSTRACT FROM AUTHOR]