arXiv subjects

S. H. Shekh

Publications and source records attributed to S. H. Shekh.

At least 19 recordsLinked to original sources

arXiv2026

A Nonsingular Logarithmic Bouncing Cosmology in $f(R,T)$ Gravity with Thermodynamic Viability

We present a nonsingular bouncing cosmological model in the framework of modified $f(R,T)$ gravity within a spatially flat Friedmann--Robertson--Walker universe. A logarithmic time-dependent scale factor is assumed to realize a smooth transition from a contracting phase to an expanding phase without encountering an initial singularity. Based on this assumption, the dynamical evolution of the Hubble parameter, deceleration parameter, energy density, and pressure is obtained for various choices of the model and the matter--geometry coupling parameter to confirm the occurrence of a successful bounce. The effective equation of state parameter is examined to characterize the cosmic fluid during different evolutionary phases. The violation of energy conditions, necessary for the realization of the bouncing behavior, is also discussed. The stability of the model is investigated using the squared speed of sound and is found to remain positive within the allowed parameter space, indicating classical stability. Furthermore, constraints on the matter--geometry coupling parameter are obtained by demanding positive energy density, negative pressure, and a viable cosmological evolution. The obtained cosmological constraint on the coupling parameter is also shown to be compatible with the currently available compact-object constraints. The thermodynamic behavior of the model is examined by testing the generalized second law of thermodynamics. The total entropy production rate remains negative during the contracting phase and changes its sign to positive during the expanding phase. However, it becomes singular at the bouncing point, reflecting the breakdown of the standard thermodynamic description during the transition phase.

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arXiv2026

Thermodynamic implications and observational constraints of interacting $f(Q,\mathcal{T})$ gravity in FRW Universe

This work investigates the dynamical evolution of the universe within the framework of symmetric teleparallel $f(Q,\mathcal{T})$ gravity, where $Q$ is the non-metricity scalar and $\mathcal{T}$ is the trace of the energy-momentum tensor. We consider a spatially flat Friedmann-Robertson-Walker (FRW) metric and explore a specific functional form $f(Q,\mathcal{T}) = \alpha Q + \beta \mathcal{T}$ to derive the gravitational field equations. To characterize the late-time cosmic acceleration, we utilize a model-independent approach by adopting a particular Hubble parameter $H(z)$ parametrization. The model parameters are constrained using the latest observational datasets, including the Hubble ($H(z)$) measurements and Pantheon+ samples. Our results indicate a transition from a decelerated to an accelerated expansion phase. We further examine the physical viability of the model through various cosmological diagnostics such as energy density, the equation of state parameter and thermodynamic properties. The analysis demonstrates that $f(Q,\mathcal{T})$ gravity provides a consistent alternative to the $\Lambda$CDM model in explaining the current accelerated expansion of the universe.

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arXiv2026

Particle Creation and Variable Generalized Chaplygin Gas in $\mathcal{F}(\mathcal{R},\Sigma,\mathcal{T})$ Gravity

In this work, we investigate the cosmological dynamics of a spatially flat Friedmann--Lema\^itre--Robertson--Walker Universe in the framework of generalized $ \mathcal{F}(\mathcal{R},\Sigma,\mathcal{T}) $ gravity by incorporating gravitationally induced particle creation together with the variable generalized Chaplygin gas scenario. The modified gravitational action depends explicitly on the Ricci scalar $ \mathcal{R} $, the matter-coupling scalar $ \Sigma $, and the trace of the energy--momentum tensor $ \mathcal{T} $, which collectively generate significant corrections to the standard cosmological evolution. The particle creation mechanism is introduced through an open thermodynamic description of the Universe. In addition, the dark sector is modeled using the variable generalized Chaplygin gas formalism. To examine the observational consistency of the model, the free parameters are constrained using the Pantheon$^+$ Type Ia Supernova compilation together with the combined observational Hubble and Pantheon$^+$ datasets through a statistical $\chi^2$-analysis. The cosmological behavior of the model is further explored through the evolution of the cosmological parameters. Furthermore, the thermodynamic properties of the model are investigated using the apparent horizon formalism. The obtained results demonstrate that the entropy evolution remains physically consistent throughout the cosmic evolution. Hence, the present $ \mathcal{F}(\mathcal{R},\Sigma,\mathcal{T}) $ gravity framework with particle creation provides a viable geometrical description of the late-time accelerated Universe and remains compatible with recent cosmological observations.

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arXiv2026

Anisotropic Cosmology with interacting Dark Energy in f(R,T) Gravity: A Data-Constrained & independent Approach

In this work, we investigate the cosmological dynamics of an anisotropic Universe within the framework of $f(R,T)$ gravity by incorporating pressureless dark matter and the dark energy models. The analysis is carried out in a Bianchi type-I space-time, allowing us to capture possible deviations from isotropy and their evolution during cosmic expansion. A phenomenological reconstruction scheme based on a variable deceleration parameter is adopted to derive a redshift-dependent Hubble function. To establish observational viability, we constrain the free parameters of the model using a comprehensive statistical analysis that combines observational Hubble data and the Pantheon+ Type Ia supernova compilation. The resulting parameter space is tightly bounded, and the reconstructed expansion history exhibits strong consistency with current observational expectations. The model successfully reproduces the transition from an early decelerating phase to the present accelerated epoch, while asymptotically approaching a de Sitter-like regime. Further we analyzed the geometrical diagnostics, including the statefinder and $O_m$ diagnostics, which indicate a close correspondence with the standard $\Lambda$CDM scenario at late times. The behavior of the effective equation of state suggests a dynamically evolving dark energy component consistent with a quintessence-like regime. Additionally, the analysis of energy conditions confirms the physical admissibility of the model, whereas the stability investigation reveals the presence of classical instabilities at the perturbative level.

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arXiv2026

Comparative Study of $f(T)$ Gravity Models with Observational Constraints from \textit{OHD} and \textit{Pantheon+ datasets}

The late-time acceleration of the universe remains one of the most significant open problems in modern cosmology. Modified gravity frameworks such as $f(T)$ gravity provide a geometric alternative to dark energy by attributing cosmic acceleration to torsional effects. In this study, we present a comparative analysis of three different forms of $f(T)$ models: (i) a simple power-law form $f(T) = \eta (-T)^{n}$, (ii) the exponential form $f(T) = \beta T_{0}\left(1-e^{-p \sqrt{T/T_{0}}}\right)$ and (iii) a logarithmic form $f(T) = \gamma T \ln\!\left(\frac{T}{T_{0}}\right)$. Using parameterization of the deceleration parameter $q(z)$ and the corresponding $H(z)$ expression, we constrain the model parameters with the recent Hubble parameter and BAO data through a Markov Chain Monte Carlo (MCMC) approach. The physical behavior of the effective energy density, equation of state parameter, squared sound speed, cosmological $Om(z)$ diagnostics, and energy conditions (NEC, DEC, SEC) were investigated for all three models. Our comparative analysis shows that all models asymptotically approach the $\Lambda$CDM behavior at late times, while they differ in stability properties and energy condition behaviors. In particular, the violation of the strong energy condition (SEC) has emerged as a common feature consistent with current accelerated expansion. This study highlights how different $f(T)$ functional forms can yield distinct cosmological dynamics while maintaining consistency with observational data.

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arXiv2026

Interacting Ghost Dark Energy with Sign-Changeable Coupling in Brans-Dicke Cosmology

In this study, we analyze the ghost dark energy model in Brans-Dicke cosmology in the framework of a flat Friedmann-Lemaitre-Robertson-Walker universe. We consider an interaction between ghost dark energy and dark matter with a sign-changeable interaction term. To discuss the cosmological implications of the model, we consider a well-motivated logarithmic form of the Brans-Dicke scalar field. By deriving the cosmological evolution equations, we obtain the cosmological parameters such as the equation of state and deceleration parameters. We analyze the behavior of the cosmological parameters by plotting their graphs against the redshift parameter ($z$). We observe that the equation of state parameter shows quintessence-like behaviour during present and future epochs; however, phantom-like behavior is also possible for suitable values of the model parameters. Analysis of the deceleration parameter shows a smooth recent phase transition of the universe (deceleration to acceleration). An interesting result we observe is the decelerated expansion of the universe in the far future, i.e, the universe experiences another phase transition in the future. The physical significance of the well-known cosmological plane ($w_D-w_D'$ plane) is discussed in our model. We observe that the trajectories start in the freezing region with the same initial behavior, deviate from each other during the evolution and ends in the thawing region. Finally, we perform a detailed thermodynamic analysis and demonstrate that the generalized second law of thermodynamics is satisfied within the present interacting ghost dark energy model.

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arXiv2025

Effective $\Lambda$CDM model emerging from $f(Q,T)$ under a special EOS limit in symmetric cosmology with Bayesian and ANN observational constraints

In this work, we investigate the cosmological consequences of an effective $\Lambda$CDM model emerging from the more general $f(Q,T)$ gravity theory under the special equation-of-state condition $\rho + p = 0$. Under this limit, the field equations yield the constraint $F(Q,T)H(t)=C$, implying that the function $F=f_Q$ becomes purely dependent on the non-metricity scalar $Q$, and the background evolution mimics that of the standard $\Lambda$CDM model. We derive the resulting functional forms of $f(Q)$, obtain the corresponding effective cosmological constant, and analyze the physical nature of this reduction. To test the model against observations, we perform a background-level parameter estimation for $H_{0}$ and $\Omega_{m}$, and evaluate the derived parameter $S_{8}$ (anchored to the Planck baseline $\sigma_8$) using cosmic chronometers (CC), baryon acoustic oscillations (BAO), and Pantheon+ SN Ia datasets. A dual-pipeline analysis is carried out using conventional Bayesian Markov Chain Monte Carlo (MCMC) sampling alongside a machine-learning based Artificial Neural Network (ANN) emulator deployed as a complementary consistency check. We demonstrate that the ANN approach successfully emulates the continuous parameter space with high computational efficiency, yielding results in close agreement with the standard MCMC likelihood framework. Because the background evolution strictly mimics the standard $\Lambda$CDM paradigm, the model successfully reproduces recent observational trends and recovers standard parameter constraints without dynamically resolving the baseline $H_{0}$ and $S_{8}$ tensions. Our results indicate that effective $\Lambda$CDM scenarios derived from $f(Q,T)$ gravity provide a viable and consistent with recent observational data.

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arXiv2025

Cosmological Evolution of Viscous Dark Energy in f(Q,C) Gravity: Two-Fluid Approach

In this paper, we study the cosmological evolution of a viscous dark energy model within the framework of $f(Q, C)$ gravity, utilizing a two-fluid approach. The model incorporates non-metricity and boundary contributions to the total action, represented by the scalar quantities $Q$ and $C$. The viscosity in the dark energy fluid is modeled to understand the impact of bulk viscosity on cosmic expansion and the late-time acceleration of the universe. We derive the field equations using the modified FLRW metric and analyze the behavior of key cosmological parameters, including the energy density, pressure, and the equation of state (EoS) parameter. The effective EoS parameter is also studied in the context of cosmic evolution. We impose observational constraints on the Hubble parameter $H(z)$ using recent datasets from DESI-Y1, SDSS-IV, Pantheon+ (without SHOES calibration), and cosmic chronometer measurements. The analysis shows that the model effectively describes the universe's expansion history and predicts a transition from deceleration to acceleration, consistent with observational data. This model also provides an alternative explanation for cosmic acceleration without the need for a cosmological constant.

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arXiv2025

Generalized Second Law and Thermodynamical Aspects of $f(Q,\mathcal{T})$ Gravity

Late-time cosmic acceleration has motivated the exploration of various extensions of general relativity, among which $f(Q,\mathcal{T})$ gravity, based on the non-metricity scalar $Q$ and the trace of the energy--momentum tensor $\mathcal{T}$, has gained increasing attention. In this study, we explore the thermodynamic aspects of $f(Q,\mathcal{T})$ gravity by establishing the first law and generalized second law of thermodynamics at the apparent horizon of a flat FLRW universe. By applying the Gibbs relation, we determined the rate of change of the total entropy and assessed the conditions under which the generalized second law remains valid for various choices of $f(Q,\mathcal{T})$. Our analysis focuses on linear, power-law, quadratic trace, exponential, and cross-coupling models, inspired by frameworks such as $f(R,\mathcal{T})$, $f(T)$, and modifications motivated by string theory. Our analysis showed that linear and mildly nonlinear models are generally thermodynamically consistent, whereas strongly nonlinear or interaction-type models require fine-tuned parameters for the generalized second law to hold. The present analysis underscores that thermodynamic considerations serve as effective criteria for assessing the viability of modified gravity models and their relevance to cosmological dynamics.

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arXiv2025

Dark Energy Behavior from Static Equation of State in Non-Minimally Coupled Gravity with Scalar Deformation

In this study, we explore the cosmological implications of a modified gravity theory characterized by the function $ f(R, \Sigma, T) $, where $ R $ is the Ricci scalar, $ \Sigma $ represents a geometric deformation term, and $ T $ denotes the trace of the energy-momentum tensor. The model is reconstructed under the framework of three fundamental energy conditions: Null Energy Condition (NEC), Dominant Energy Condition (DEC), and Strong Energy Condition (SEC). We derive the corresponding Hubble parameter $ H(z) $ for each case and constrain the free parameters $ H_0 $, $ \alpha $, and $ \beta $ using the latest Cosmic Chronometer (CC) and Pantheon+ Type Ia Supernova datasets. A thorough analysis of physical quantities such as pressure, energy density, and the equation of state parameter is carried out. Furthermore, diagnostic tools including the deceleration parameter $ q(z) $, statefinder parameters $ \{r, s\} $, and the $O_m(z)$ diagnostic are employed to assess the models viability. Our findings suggest that the model can consistently describe late-time cosmic acceleration and offers distinct behavior under different energy conditions, all while aligning with current observational data.

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arXiv2025

Cosmological Analysis of $f(R, \Sigma, T)$ Gravity with EoS Parameterization

In this paper, we present a comprehensive cosmological analysis within the framework of $f(R, \Sigma, T)$ gravity, a modified theory that incorporates nonlinear matter-geometry coupling via the inclusion of both the trace of the energy-momentum tensor $T$ and the scalar $\Sigma = T_{\mu\nu}T^{\mu\nu}$. We consider a spatially flat Friedmann-Robertson-Walker (FRW) universe and introduce a linear parameterization for the equation of state (EoS) parameter based on the Chevallier-Polarski-Linder (CPL) form, which allows us to explore the dynamical evolution of dark energy without imposing restrictive assumptions. To confront the theoretical model with observations, we utilize the latest Hubble parameter measurements from cosmic chronometers. The model parameters are constrained using Markov Chain Monte Carlo (MCMC) simulations with the \texttt{emcee} package, leading to tight bounds on the parameters. The analysis reveals that the model remains consistent with the $\Lambda$CDM scenario while allowing mild deviations consistent with observational data. Furthermore, we examine the physical and kinematical features of the model by studying the behavior of the physical parameters. Finally, the calculated age of the universe within this framework is found to be in excellent agreement with Planck 2018 results, highlighting the and viability of $f(R, \Sigma, T)$ gravity as a candidate for explaining late-time cosmic acceleration.

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arXiv2025

Dark Energy Phenomenology in a $f(R,\Sigma,T)$ Gravity Framework: $O_m(z)$ Parameterization Approach

This study investigates the cosmological implications of $f(R,\Sigma,T)$ gravity by reconstructing the Hubble parameter from a logarithmic parameterization of the $O_m(z)$ diagnostic. Our approach offers a model-independent way to probe the nature of dark energy and differentiate it from a cosmological constant. We derive the field equations for $f(R,\Sigma,T) = R + \Sigma + 2\pi\eta T$ within the homogeneous, isotropic, and spatially flat Friedmann-Robertson-Walker (FRW) metric. A comprehensive analysis of key physical parameters, including the equation of state (EoS) parameter $\omega(z)$, the $(\omega-\omega')$-plane, the squared sound speed $\vartheta^2$, and various energy conditions (Null, Dominant, Strong), is presented. Our findings reveal a dynamic EoS parameter that consistently remains within the quintessence regime ($-1 < \omega < -1/3$), approaching $\omega = -1$ in the far future, thereby avoiding phantom behavior and maintaining the weak energy condition. The model successfully reproduces the cosmic transition from deceleration to acceleration, as indicated by the deceleration parameter $q(z)$ crossing zero. While the model aligns well with observational data for cosmic expansion, the analysis of $\vartheta^2$ indicates classical instability, a point requiring further theoretical refinement. Overall, this work demonstrates the viability of $f(R,\Sigma,T)$ gravity as a framework capable of describing the universe's accelerated expansion, consistent with current cosmological observations, while offering a dynamic alternative to the $\Lambda$CDM model.

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arXiv2025

Cosmological Implications of $f(R,Σ, T)$ Gravity: A Unified Approach Using OHD and SN Ia Data

This paper investigates the cosmological implications of the modified gravity framework known as $f(R,Σ, T)$ gravity, focusing on its potential to unify and extend current cosmological models. The theory, introduced by Bakry and Ibraheem in 2023, combines the Ricci scalar, a scalar parameter representing torsion or other geometric properties, and the trace of the energy-momentum tensor. By analyzing observational Hubble data (OHD) and the Pantheon compilation of Type Ia Supernovae (SN Ia), we explore how this framework provides the accelerated expansion of the universe, the nature of dark energy, and phenomena like the Big Rip singularity. Employing the Friedmann-Robertson-Walker (FRW) metric and solving the modified field equations, we derive key cosmological parameters such as the Hubble constant and matter energy density parameter. These parameters are constrained through statistical analysis of observational data, yielding and from OHD, and and from SN Ia. The evolution of the equation of state (EoS) parameter, isotropic pressure, and energy density is also investigated. By considering energy conditions and stability criteria, the study highlights the viability of gravity as an alternative framework to General Relativity and models. Our findings affirm the model's compatibility with current observational evidence and its potential to the universe's past and future dynamics.

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arXiv2025

Dark Energy and Cosmic Evolution: A Study in f (R, T) Gravity

In the context of f(R, T) gravity theory for the flat Friedmann Lemaitre Robertson Walker (FLRW) model, the accelerating expansion of the universe is investigated using a specific form of the emergent Hubble parameter. Datasets from H(z), Type Ia supernovae (SNIa), and Baryon Acoustic Oscillations (BAO) are used to constrain the model and identify the ideal parameter values in order to evaluate the statistical significance of f(R, T) gravity. The best-fit parameters are derived by solving the modified Friedmann equations through a MCMC analysis. These parameters are used to compute the equation of state, statefinders, energy conditions, and the (w-w) plane. Furthermore, the evolution of kinematic cosmographic parameters is examined. The findings provide significant behavior and features of dark energy models. Our comprehension of the dynamics and evolution of the universe is improved by this study, which also advances our understanding of dark energy and how it shapes the universe.

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arXiv2024

Probing Dark Energy Properties in $f Q,C)$ Gravity with FLRW Cosmological Models

This study delves into the cosmological implications of the $f(Q,C)$ modified gravity framework within the context of the FLRW spacetime which offers a dynamic alternative to the standard $\Lambda$CDM cosmology. Here, we define the transit form of Hubble's parameter to explain several geometrical and physical aspects. The chosen parametric form of the Hubble parameter represents a smooth transition from the decelerating early universe to the accelerating present and late-time evolution. Employing observational datasets such as the Hubble parameter, Type Ia supernovae, Baryon Acoustic Oscillations (BAO), and Standard Candles (SC), we constrain the model parameters using the Markov Chain Monte Carlo (MCMC) method. The isotropic pressure, energy density, equation of state parameter, and energy conditions were analyzed to explore the physical viability of the $f(Q,C)$ framework. The results highlight the model's ability to replicate key cosmological behaviors, including the accelerated expansion driven by dark energy.

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arXiv2024

Probing Dark Energy Properties with Barrow Holographic Model in f(Q, C) Gravity

Understanding the accelerating expansion of the universe remains one of the foremost challenges in modern cosmology. This study investigates Barrow Holographic Dark Energy (BHDE), a model inspired by quantum gravitational corrections, within the framework of $f(Q,C)$ gravity. This extension of symmetric teleparallel gravity incorporates the non-metricity scalar $Q$ and the boundary term $C$, enabling a deeper exploration of cosmic dynamics without relying on a cosmological constant or exotic matter. The BHDE model is analyzed under a flat Friedmann-Robertson-Walker (FRW) metric, focusing on key cosmological parameters such as energy density, isotropic pressure, the equation of state (EoS) parameter, stability conditions and the energy conditions. The results demonstrate that the EoS parameter transitions from matter-like behavior ($z > 0$) to negative values at $z = 0$, indicating the dominance of dark energy and its role in the universe's accelerated expansion. As $z$ approaches $-1$, the EoS parameter asymptotically converges to $-1$, aligning with the $Λ$CDM model. This work underscores the potential of the BHDE model in $f(Q,C)$ gravity as a comprehensive framework for studying cosmic acceleration. By incorporating Barrow entropy and addressing the interplay between non-metricity and boundary terms, the model provides a dynamic approach to explaining dark energy.

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arXiv2024

Exploring Phase Space Trajectories in $Λ$CDM Cosmology with f(G) Gravity Modifications

In this work, the cosmic solutions, particularly the well-known $Λ$CDM model, are investigated in the framework of the Gauss-Bonnet gravity, where the gravitational action incorporates the Gauss-Bonnet invariant function. We utilize a specialized formulation of the deceleration parameter in terms of the Hubble parameter $H$, given by $q = -1 - \frac{\dot{H}}{H^2}$, to solve the field equations. To identify the appropriate model parameters, we align them to the most recent observational datasets, which include 31 data points from the Cosmic Chronometers, Pantheon+, and BAO datasets. The physical characteristics of the cosmographic parameters, such as pressure and energy density, that correlate to the limited values of the model parameters, are examined. The evolution of the deceleration parameter suggests a transition from a decelerated to an accelerated phase of the universe. Additionally, we examine the stability of the assumed model and provide an explanation for late-time acceleration using the energy conditions. The behavior of the equation of state parameter has been analyzed through dynamical variables by constraining various parameters in light of the recent observational data. This study has resulted in a quintessence-like evolution.

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arXiv2024

Modelling the Accelerating Universe with $f(Q)$ Gravity: Observational Consistency

In this paper, we present a cosmological model within the framework of symmetric teleparallel gravity, focusing on $f(Q)$ gravity, where $Q$ represents the non-metricity scalar. Utilizing cosmological datasets, we derive an accelerating cosmological model by constraining its free parameters. To achieve this, we determine the parametric form of the Hubble parameter using a well-motivated $f(Q)$ function. Remarkably, all obtained values fall within the range suggested by cosmological observations. By employing the best-fit parameters, we calculate the present geometrical parameters and demonstrate the accelerating behaviour of the Universe. Furthermore, we thoroughly examine the evolutionary behaviours of the Universe, noting that our model converges to the $Λ$CDM model at late times. Finally, we investigate the energy conditions and find a violation of the strong energy condition, which could provide a valuable understanding of the nature of dark energy.

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