The evolution of the deceleration parameter q(z) plays a crucial role in understanding the dynamics of dark energy within the framework of modern cosmology. In this study, we perform a parametric reconstruction of q(z) in a spatially flat Friedmann–Robertson–Walker (FLRW) Universe composed of radiation, pressureless dark matter, and dark energy. We consider a physically motivated form of q(z) that effectively describes the transition of the Universe from a decelerating to an accelerating expansion phase. This parametrization is incorporated into the Friedmann equations to derive the corresponding Hubble parameter, which is then confronted with a comprehensive set of observational data, including Hubble parameter measurements H(z), Type Ia supernovae (SNIa), and Baryon Acoustic Oscillations (BAO) data. Employing the Markov Chain Monte Carlo (MCMC) approach, we constrain the model parameters using the combined H(z)+SNIa+BAO dataset. The best-fit parameters are subsequently used to reconstruct the cosmographic quantities, such as the deceleration, jerk, and snap parameters, which provide deeper insight into the expansion history of the Universe. Finally, a comparative analysis with the standard ΛCDM model is carried out to assess the compatibility and effectiveness of the proposed parametrization.

In this paper, we study the late-time cosmic expansion within a scalar-field dark energy framework in a spatially flat FLRW Universe by adopting a quadratic parametrization of the deceleration parameter [Formula: see text]. This approach allows a controlled and analytical description of the transition from decelerated to accelerated expansion. The model parameters are constrained using MCMC analysis with combined CC, BAO, and standard candle data (SnIa, QSO, GRBs, and [Formula: see text] measurements). The results indicate a transition redshift [Formula: see text] and a present-day value [Formula: see text]. The reconstructed equation-of-state parameter satisfies [Formula: see text], confirming a quintessence-like behavior. The scalar field evolves monotonically, while the reconstructed potential [Formula: see text] remains smooth and exhibits a regular evolution over the considered field range. The model is statistically competitive ([Formula: see text]) and yields [Formula: see text] [Formula: see text]km s[Formula: see text] Mpc[Formula: see text], highlighting the flexibility of the proposed dynamical dark-energy parametrization and its consistency with current observations. These results support the proposed parametrization as a viable quintessence dark energy scenario consistent with observations.

This study explores the late-time accelerated expansion of the universe and the evolution of cosmic structures in the context of a particular f(R,& Laplacetrf;(m)) gravity model - an extended gravitational framework in which the standard Einstein-Hilbert action is generalized by incorporating a nonlinear coupling between spacetime curvature and matter fields. The specific form of the gravitational action is chosen as f(R,& Laplacetrf;(m)) = (R)/(2) + & Laplacetrf;(n)(m) - beta, where n and beta are free model parameters, and the corresponding equations of motion are derived assuming a matter-dominated cosmological condition. The study is formulated for a spatially flat FLRW universe, where we derive an exact analytical solution to the field equations. We constrain the model parameters using advanced Markov Chain Monte Carlo techniques, employing a combined dataset of BAO, cosmic chronometers, and standard candles. Furthermore, we examine the behavior of physical parameters that describe the various phases of cosmic evolution, including the deceleration parameter q, jerk j, and snap s parameters and also the statefinder pairs (s,r) and (q,r). We determine the transition redshift at which the cosmic expansion shifts from decelerating to accelerating, with a resulting value of z(tr) = 0.652. Statefinder diagnostics show that the f(R,& Laplacetrf;(m)) model follows a simple trajectory, lies in the quintessence region. These findings underscore the significance of f(R,& Laplacetrf;(m)) gravity in explaining cosmic acceleration, without requiring a cosmological constant, and offering a promising framework for future explorations of dark energy and the evolution of the universe.

In this work, we investigate the cosmological implications of f(Q) gravity by introducing a nonlinear equation of state of the form p=beta rho(2)-rho. This modified gravity framework, based on the non-metricity scalar Q, offers an alternative to General Relativity and provides new insights into cosmic acceleration. To test the validity of our model, we use a combined observational dataset consisting of 31 cosmic chronometer data points, 1701 Type Ia supernova measurements, and 26 baryon acoustic oscillation observations, leading to a total of 1758 data points. The statistical analysis based on this dataset allows for a viable comparison with the standard Lambda CDM model. We analyze cosmographic parameters such as the deceleration parameter, jerk parameter, and statefinder parameters, to determine the impact of the model on the evolution of the universe. The results indicate that our model successfully describes cosmic expansion while presenting deviations from the standard Lambda CDM scenario. Statistical comparisons based on the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) further suggest that the proposed model provides a competitive fit to observational data. Our findings show the potential of f(Q) gravity with a nonlinear EoS in the quadratic form as an alternative to the Lambda CDM model. This work contributes to efforts to explore modified gravity theories as possible explanations for late cosmic acceleration and provides commentary on their implications.

This paper examines dark-energy compact stars under the paradigm of modified Rastall teleparallel gravity. This is the primary analysis of dark energy celestial phenomena under this modified gravitational theory. Utilizing the torsion-based functions, f(T) and h(T), we examined their impacts within a spherically symmetric space-time designated as the inner geometry, while employing the Schwarzschild geometry as the outside space-time. This study examines several features of dark energy in stars, encompassing dark energy pressure components, energy conditions, and equation of state components. Our findings indicate that the detected adverse behavior of certain stellar parameters provided substantial evidence, ensuring the presence of dark energy in celestial configurations. Thorough examinations of energy conditions, pressure profiles, sound speeds, adiabatic index, gradients, mass function, compactness, and redshift function provide a full evaluation, confirming the viability and authenticity of the analyzed stellar configuration.

We investigate late-time cosmic acceleration within the framework of f(Q) gravity supplemented by a phenomenological nonlinear equation of state of the form p = Aρ - B√(ρ). Adopting a power-law ansatz f(Q)=γ ,(Q/Q_0)^n, we derive analytic expressions for the energy density and Hubble function and confront the model with a combined dataset consisting of CC, SNIa, BAO, quasar, and GRB observations covering 0.106

In this paper, the accelerating expansion of the universe has been investigated in the multi-components fluid in the coupling of geometry with matter alternative theory f(R, T) gravity, where the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the trace of the stress-energy tensor T. To address the late-time accelerating universe, we solve the Friedmann equations via the nonzero divergence of the energy-momentum tensor considered in the presence of a multi-component fluid. The best-fit values of the model parameters are determined using the Markov Chain Monte Carlo (MCMC) simulation using the cosmic chronometers (CC) dataset, which consists of 31 points and the recent Pantheon+ analysis of 1701 light curves of 1550 distinct Type Ia supernovae (SNIa) ranging in redshift from z = 0.001 to 2.26. The trajectory of the deceleration parameter indicates that the universe has transitioned from a deceleration phase to an acceleration phase. We also look into the behavior of the jerk and snap parameters, the statefinder analysis, the om diagnostic, and the effective EoS parameter. It is shown that the model considered is consistent with the accelerating universe and the predictions of the quintessence model at present.

The ongoing Hubble tension, a significant discrepancy between early- and late-universe measurements of the Hubble constant H0, challenges the foundations of modern cosmology. A closely related issue, the H0−rd tension, arises from the dependency of BAO-based inferences of H0 on the assumed sound horizon at the drag epoch rd. In this work, we investigate the cosmological implications of the f(R,T)=R+2λT gravity model, which introduces a direct coupling between the Ricci scalar (R) and the trace of the energy-momentum tensor (T). By utilizing a Markov Chain Monte Carlo (MCMC) analysis with observational datasets, such as Baryon Acoustic Oscillations (BAO), Cosmic Chronometers (CC), and Standard Candles (SC), we constrain the model parameters and assess their compatibility with current cosmological observations. Our findings indicate a strong correlation between H0 and rd, confirming that different dataset combinations lead to systematically varying constraints on these parameters. The inclusion of the Riess 2019 prior (R19) results in higher values of H0, reinforcing the Hubble tension, while BAO-only data favors lower values, consistent with early-universe measurements. Additionally, we analyze the evolution of the main cosmologic parameters such as the deceleration parameter q(z) and the equation of state parameter ω(z). Our results suggest that the f(R,T) model exhibits a quintessence-like behavior, with ω(z)>−1 at present, indicating a dynamical dark energy component rather than a simple cosmological constant. Furthermore, we confirm that the present-day values of the matter and dark energy density parameters, Ωm≈0.3 and ΩΛ≈0.7, remain consistent with a spatially flat universe. These results highlight the role of modified gravity in addressing key tensions in cosmology and demonstrate that the f(R,T) framework provides a natural extension of ΛCDM.

In this study, we investigate Modified Chaplygin gas solutions within the framework of f(Q) theory of gravity, a modified gravitational theory that seeks to address the limitations of the conventional Lambda cold dark matter model. f(Q) gravity offers a novel perspective on cosmic dynamics by incorporating a non-minimal coupling between the geometry and the matter, allowing for a richer understanding of the expansion of the universe. We explore the implications of modified Chaplygin gas, characterized by its unique equation of state (eos), which transitions from a matter-dominated phase to a dark energy-dominated phase, thereby influencing the evolution of the energy density and pressure across cosmic redshifts. Our findings reveal significant insights into the interplay between different energy components, highlighting the transition from positive to negative pressure as a hallmark of the role of dark energy in driving the accelerated expansion of the universe. This research not only enhances our comprehension of cosmic evolution, but also provides a compelling framework for future investigations into the nature of dark energy and its impact on the ultimate fate of the universe.

We investigate the implications of the modified gravity theory f(R,L_m) on the cosmological evolution. By examining the nonlinear model f(R,L_m)=R/2+(α R+1)L_m , we explore the impact of a nonminimal coupling between curvature and matter on the cosmic expansion. Using a parametrized deceleration parameter dependent on the redshift z , we analyze the Friedmann–Lemaître–Robertson–Walker (FLRW) universe in the f(R,L_m) framework. Through observational constraints derived from Cosmic Chronometers (CC), Type Ia Supernovae (SNIa), and Baryon Acoustic Oscillations (BAO), we perform a detailed comparison with the standard Λ CDM model. Our results show that the f(R,L_m) model is consistent with observational data, but deviations from the Λ CDM model emerge in its geometric structure, highlighting the potential of f(R,L_m) gravity in explaining the dark energy and cosmic acceleration.

We present an investigation of a scalar field dark energy model in the context of the FLRW universe, focusing on the parameterization of the deceleration parameter q(z) to study the evolution of cosmic acceleration. By employing extensive observational datasets—including 30 independent cosmic chronometer measurements, 17 additional baryon acoustic oscillation data points, and standard candle datasets from Pantheon Type Ia supernovae, Quasars, and Gamma-Ray Bursts—we provide constraints on cosmological parameters using advanced Markov chain Monte Carlo methods. Our analysis identifies a transition redshift of z_t = 0.62 , marking the shift from decelerated to accelerated expansion, with a current deceleration parameter of q_0 = -0.59 . The equation of state parameter confirms the dynamical behavior of quintessence, deviating slightly from a cosmological constant. Furthermore, the model demonstrates strong consistency with Λ CDM at lower redshifts while revealing distinct deviations at higher redshifts, which provides valuable insights into the late-time dynamics of the universe. By examining the evolution of cosmography parameters, energy density, pressure, and the scalar field equation of state, this study contributes the relevance of scalar field models as promising candidates for dark energy.

In this paper, we have established a scalar field dark energy model in the flat FLRW universe, with the aim of studying the evolution of cosmic acceleration. A parameterization of the deceleration parameter q(z) is considered. We derive constraints on cosmological parameters by applying sophisticated Markov Chain Monte Carlo (MCMC) methods through the combination of various cosmological datasets such as Baryon Acoustic Oscillation (BAO) data points, Cosmic Chronometer (CC) measurements, and Standard Candle (SC) datasets from Pantheon Type Ia supernovae (SNe Ia), Quasars and gamma-ray bursts. This analysis allows us to determine a transition redshift, from the decelerated to the accelerated universe, with a value of z(tr)=0.69 and the current value of the deceleration parameter is q(0)=-0.64. The dynamical behavior of quintessence is confirmed by the Equation of State (EoS) parameter, where -10.65. This study, through an analysis of cosmographic parameters such as energy density rho(phi), pressure p(phi), and the scalar field EoS, emphasizes the potential of scalar field models as leading candidates for dark energy. Furthermore, we observe that the model yields a slightly higher value of the Hubble constant H-0 for certain dataset combinations, indicating that it may partially alleviate the Hubble tension.

In this paper, we have studied the late-time accelerating expansion of the Universe using the matter-geometry coupled f(Q, T) gravity model, where Q is the non-metricity scalar and T represents the trace of the energy-momentum tensor. We constrain the best-fit values of cosmological parameters Ω_m0, H_0, α_0 β_0 through the Monte Carlo Markov Chain (MCMC) simulation using 31 Hubble parameter data points from cosmic chronometers (CC) and 26 data points from baryon acoustic oscillations (BAO), making a total of 57 datasets (labeled ), as well as SNIa distance moduli measurements from the Pantheon+ sample, which consists of 1701 light curves of 1550 distinct supernovae (labeled ), and their combination (labeled . We compare our constrained Hubble constant H_0 value with different late-time and early-time cosmological measurements. Deceleration parameter q(z), effective equation of state parameters w_eff(z), Hubble parameter H(z), and distance modulus μ(z) are numerical results of dynamical quantities that show that the f(Q, T) gravity model is compatible with a transition towards a quintessence-like phase in the late-time. In conformity with ΛCDM, we moreover take into account the geometrical interpretations by considering the state-finder parameters r-s and r-q, which are crucial parameters for additional analysis. Additionally, the statistical analysis has been carried out for further investigation.

In this study, we investigate the late-time isotropy of the Universe within the framework of f(Q,T) gravity. Using the Locally Rotationally Symmetric (LRS) Bianchi-I cosmological model, we explore the evolution of the Universe in an anisotropic setting with a perfect fluid source. By employing observational constraints from Baryon Acoustic Oscillations (BAO), Cosmic Chronometers (CC), and Standard Candles (SC), we analyze the viability of the model and its implications for cosmic acceleration. We derive the modified field equations in f(Q,T) gravity and specialize in the case of f(Q,T) = Q + beta T, where beta is a model parameter. We study the evolution of the Hubble parameter, deceleration parameter, and the anisotropy parameter to assess the transition from an initially anisotropic state to an isotropic Universe at late times. Our results show that the model successfully reproduces the observed cosmic expansion and provides a consistent late-time behavior, supporting the transition to isotropy. Furthermore, we place constraints on the model parameters using a Markov Chain Monte Carlo (MCMC) analysis and compare our results with the standard Lambda CDM model. The best-fit value of the deceleration parameter at present is found to be q0 = -0.7269(-0.0004)(+0.0003), indicating a Universe undergoing accelerated expansion. This study highlights the significance of alternative gravity theories in explaining cosmic evolution and suggests that f(Q,T) gravity provides a compelling framework for understanding the isotropic nature of the Universe at late times.

This study investigates the cosmological implications of the f(R,T)=R+2 lambda T gravity model. f(R,T) gravity is a modification of General Relativity (GR) that introduces a coupling between the Ricci scalar R and the trace of the energy-momentum tensor T. This work provides a comprehensive analysis of the model's predictions using updated observational data, including uncorrelated Baryon Acoustic Oscillations and Cosmic Chronometers. By employing the Markov Chain Monte Carlo technique, we constrain the model parameters, demonstrating their compatibility with current observational datasets. Our findings reveal that the model naturally extends the Lambda CDM model, with the parameter lambda from f(R,T) gravity quantifying deviations from GR. Additionally, we provide a critical discussion on the challenges and limitations of the f(R,T) framework, addressing issues such as observational constraints, systematic uncertainties and model dependencies. This work not only refines parameter constraints for f(R,T) gravity, but also bridges the gap between theoretical predictions and observational tests, offering a powerful framework for exploring deviations from GR in a cosmological context.

This paper investigates the late-time cosmic dynamics using the matter-geometry coupled f(Q,T) gravity model, where Q is the non-metricity scalar and T represents the trace of the energy-momentum tensor. We consider the paradigm power law f(Q,T)-gravity model, f(Q,T) = -αQ−βT2/H02+η0 (where α, β and η0 are constants) to calculate the best-fit values of cosmological parameters Ωm, H0, α, β, rd and M through the Monte Carlo Markov Chain (MCMC) simulations using cosmic chronometers (CC) baryon acoustic oscillation (BAO) taken from Dark Energy Spectroscopy Instrument (DESI) and the SNIa distance moduli measurements from the Pantheon + SH0ES, which consists of 1701 light curves of 1550 distinct supernovae. Some key cosmological parameters: the deceleration parameter q(z), effective equation of state parameters weff(z), Hubble parameter H(z), and distance modulus μ(z) are presented. These dynamical quantities show that the f(Q,T)-gravity model is compatible with transitioning towards a quintessence-like phase in the late-time. In conformity with ΛCDM, we moreover take into account the geometrical interpretations by considering the state-finder parameters r−s and r−q, which are crucial parameters for additional analysis. Additionally, the statistical analysis has been carried out for further investigation of the viability f(Q,T)-gravity model.

This paper analyzes a robust parameterization of the deceleration parameter, which leads to the development of dark energy models showing very interesting features of the late-time accelerating universe. In this model, using the updated cosmic observational datasets, the tightness of the constraints is established based on a Bianchi type-I bulk viscous model with decaying cosmological term. The proposed model shows very good agreement with recent observational data. We find the best fit values of the model parameters through the MCMC method using CC, SNIa and BAO (DESIY1, and SDSS-IV) data. The constrained model values are analyzed to determine the key cosmological parameters, including the present deceleration parameter, the Hubble constant, and the transition redshift from deceleration to acceleration. Additionally, the evolution of the physical and geometrical parameters is traced by diagnostic analysis and illustrated by means of plots.

In recent decades, there has been significant research on the role of torsion in gravity, with a focus on aligning gravity with its gauge formulation and including spin into a geometric description. In order to account for the present phenomenon of the universe's accelerated expansion, recent developments have introduced f(T) theories that rely on the disparities found in teleparallel gravity. Torsion, rather than curvature, is the fundamental geometric property that describes gravity in these theories. When compared to theories involving f(R) functions, the field equations are consistently of second order and surprisingly simple. We consider a specific type of function called torsion, which is defined as f(T) = T - alpha T-0[{1 + ( T/T-0 )(2)}(-n) - 1]. The expression consists of two free parameters, n and alpha, and the current value of the torsion scalar, T-0. In order to solve the modified torsion field equations (MTFEs), we can utilize the parametrization of the deceleration parameter (DP) in terms of redshift, denoted as q(z) = q(0) + q(1)(z). Here, q(0) and q(1) represent the model parameters. The model parameters are determined by utilizing observable constraints, including as 57 Hubble data points, 1048 Pantheon supernovae type Ia data, and Baryon Acoustic Oscillations (BAO) datasets. In addition, we utilize Markov Chain Monte Carlo (MCMC) methods for statistical analysis.