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In this work, the cosmic solutions, particularly the well-known $\Lambda$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., Comment: 15 pages, 12 figures

This paper is devoted to examining cosmological bouncing scenarios in the framework of the recently proposed symmetric teleparallel gravity (or $f(Q)$ gravity), where the non-metricity scalar $Q$ represents the gravitational interaction. We assume an $f(Q)$ model in the form of $f(Q)=\alpha Q^n$, where $\alpha$ and $n$ are free model parameters. To obtain a bouncing universe, we consider a special form of the scale factor $a(t)$ in terms of cosmic time, specifically $a(t) = (1+\lambda t^2)^{1/3}$, where $\lambda$ is an arbitrary constant. We derive the field equations for the flat FLRW universe and obtain the corresponding exact solution. We investigate the physical behavior of various cosmological parameters such as the deceleration parameter, pressure, and equation of state (EoS) parameter with the energy conditions for our bounce cosmological model. Furthermore, we investigate the behavior of the perturbation terms $\delta_m(t)$ and $\delta(t)$ with respect to cosmic time $t$ using the scalar perturbation approach. We found that although the model exhibits unstable behavior at the beginning for a brief period, it shows mostly stable behavior for most of the time. Finally, we conclude that the EoS parameter crosses the quintom line $\omega=-1$ in the vicinity of the bouncing point $t=0$, which confirms the success of our bounce cosmological model., Comment: The European Physical Journal Plus accepted version

In the present analysis, we explore a new version of dark energy called Barrow holographic dark energy within the framework modified gravity called $f(Q,T)$ gravity by adopting the simple homogeneous, isotropic, and spatially flat Friedmann-Robertson-Walker (FRW) model of the universe. Our goal is to understand how the universe evolved over time. To do this, we use parameterizetion of Hubble's parameter method. We then use a powerful tool called Monte Carlo Markov Chain to find the best values for the constants in our formula. We do this by comparing our formula to actual data from observations of the universe. Once we have the best values for the constants, we calculate other important parameters that describe the universe's evolution. These include: Deceleration parameter which measures how quickly the expansion is slowing down. We found $q_0 = -0.601^{+0.0131}_{-0.0131}$. Equation of state parameter to measures the properties of dark energy. We find $\omega_0 = -0.7018^{+0.0101}_{-0.0101}$. We also study the stability and energy conditions along with the state-finder and $O_m(z)$-parameter of our model to ensure it's consistent with our understanding of the universe., Comment: 11 pages, 7 figures. arXiv admin note: text overlap with arXiv:2408.00022

This paper explores models of the FLRW universe that incorporate a time-varying cosmological term $\Lambda(t)$. Specifically, we assume a power-law form for the cosmological term as a function of the scale factor: $\Lambda(t)=\Lambda_{0} a(t)^{-\alpha}$, where $\Lambda_{0}$ represents the present value of the cosmological term. Then, we derive an exact solution to Einstein's field equations within the framework of $\Lambda(t)$CDM cosmology and determine the best-fit values of the model parameters using the combined $H(z)$ + SNe Ia dataset and MCMC analysis. Moreover, the deceleration parameter demonstrates the accelerating behavior of the universe, highlighting the transition redshift $z_{tr}$, at which the expansion shifts from deceleration to acceleration, with confidence levels of $1-\sigma$ and $2-\sigma$. In addition, we analyze the behavior of the Hubble parameter, jerk parameter, and $Om(z)$ diagnostic. Our analysis leads us to the conclusion that the $\Lambda(t)$CDM model is consistent with present-day observations., Comment: Advances in Space Research accepted version

The study conducted in this research paper utilizes the $f(Q,T)$ gravity, where $Q$ represents non-metricity and $T$ represents the trace of the energy-momentum tensor, to investigate the accelerated expansion of the universe. To complete the study, an effective EoS with one parameter $\alpha$, is parameterized as $\omega _{eff}=-\frac{3}{\alpha (1+z)^{3}+3}$. The linear version of $f(Q,T)=-Q+\sigma T$ is also considered, where $\sigma$ is a constant. By constraining the model with six BAO points, 57 Hubble points, and 1048 Pantheon sample datasets, the parameters $\alpha$ and $\sigma$ are determined to best match the data. The cosmological parameters and energy conditions for the model are derived and examined. The results show that the model is in good agreement with observations, and can serve as a valuable starting point for analyzing FLRW models in the $f(Q,T)$ theory of gravity., Comment: Chinese Journal of Physics accepted version

In this article, we introduce an innovative parametric representation of the Hubble parameter, providing a model-independent means to explore the dynamics of an accelerating cosmos. The model's parameters are rigorously constrained through a Markov Chain Monte Carlo (MCMC) approach, leveraging a comprehensive dataset consisting of 31 data points from cosmic chronometers (CC), 1701 updated observations of Pantheon supernovae type Ia (SNeIa), and 6 data points from baryonic acoustic oscillations (BAO). Our analysis delves into the behavior of various cosmological parameters within the model, including the transition from a decelerating phase to an accelerating one, as well as the density parameters and the equation of state (EoS) parameter. The outcomes of our investigation reveal that the equation of state parameter aligns with characteristics reminiscent of the phantom model, supporting the prevailing understanding of our universe's current state of acceleration. This research contributes valuable insights into the ongoing cosmic expansion and underscores the utility of our novel parametric approach., Comment: Journal of High Energy Astrophysics accepted version

In this work, we investigate the bouncing behavior of the universe within the framework of $f(R,L_m)$ gravity, using a simple form of $f(R,L_m)=\frac{R}{2}+L_m^\gamma$ (where $\gamma$ is a free model parameter) as previously studied. The model predicts a vanishing Hubble parameter in the early and late times, with the deceleration parameter approaching a specific limit at the bouncing point. The EoS parameter is observed to cross the phantom divide line ($\omega=-1$) near the bouncing point, indicating a significant transition from a contracting to an expanding phase. The model satisfies the necessary energy conditions for a successful bouncing scenario, with violations indicating exotic matter near the bouncing point. Stability conditions are satisfied for certain values of $\gamma$ near the bouncing point, but potential instabilities in late-time evolution require further investigation. Finally, we conclude that the $f(R,L_m)$ gravity model is promising for understanding the universe's dynamics, especially during events like the bouncing phase., Comment: International Journal of Geometric Methods in Modern Physics accepted version

In this paper, we investigate the cosmological implications and constraints of Weyl-type $f(Q, T)$ gravity. This theory introduces a coupling between the non-metricity $Q$ and the trace $T$ of the energy-momentum tensor, using the principles of proper Weyl geometry. In this geometry, the scalar non-metricity $Q$, which characterizes the deviations from Riemannian geometry, is expressed in its standard Weyl form $\nabla _{\mu }g_{\alpha \beta }=-w_{\mu }g_{\alpha \beta }$ and is determined by a vector field $w_{\mu }$. To study the implications of this theory, we propose a deceleration parameter with a single unknown parameter $\chi$, which we constrain by using the latest cosmological data. By solving the field equations derived from Weyl-type $f(Q, T)$ gravity, we aim to understand the behavior of the energy conditions within this framework. In the present work, we consider two well-motivated forms of the function $f(Q, T)$: (i) the linear model represented by $f(Q, T) = \alpha Q + \frac{\beta}{6\kappa^2} T$, and (ii) the coupling model represented by $f(Q, T) = \frac{\gamma}{6H_0^2 \kappa^2} QT$, where $\alpha$, $\beta$, and $\gamma$ are free parameters. Here, $\kappa^2 = \frac{1}{16\pi G}$ represents the gravitational coupling constant. In both of the models considered, the strong energy condition is violated, indicating consistency with the present accelerated expansion. However, the null, weak, and dominant energy conditions are satisfied in these models., Comment: Astronomy and Computing accepted version

The cosmic acceleration observed in the expansion of the Universe has sparked extensive research into the nature of dark energy, which is known to constitute approximately 70\% of the Universe's energy content. In this study, we explore two parametrizations of the Hubble parameter, namely power-law and logarithmic corrections, as alternatives to the standard $\Lambda$CDM model. Using observational data from Cosmic Chronometers (CC), Pantheon+, and the Baryonic Acoustic Oscillations (BAO) datasets, we investigate the dynamics of essential cosmological parameters, including the deceleration parameter, energy density, pressure, and equation of state (EoS) parameter. The $Om(z)$ diagnostic test is employed to classify different dark energy models. Our cosmological models, with the power-law and logarithmic corrections, are found to provide a good fit to the recent observational data and efficiently describe the cosmic expansion scenario., Comment: The European Physical Journal Plus accepted version

We propose a specialized parameterization for the Hubble parameter, inspired by $\Lambda$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 6 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 $0.55$, $1.5$, 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., Comment: Special Issue Celebrating the 20th Anniversary of IJGMMP

In this study, we investigate the dynamics of the Universe during the observed late-time acceleration phase within the framework of the Weyl-type $f(Q,T)$ theory. Specifically, we consider a well-motivated model with the functional form $f(Q,T)=\alpha Q+\frac{\beta }{6\kappa ^2}T$, where $Q$ represents the scalar of non-metricity and $T$ denotes the trace of the energy-momentum tensor. In this context, the non-metricity $Q_{\mu\alpha\beta}$ of the space-time is established by the vector field $w_\mu$. The parameters $\alpha$ and $\beta$ govern the gravitational field and its interaction with the matter content of the Universe. By considering the case of dust matter, we obtain exact solutions for the field equations and observe that the Hubble parameter $H(z)$ follows a power-law behavior with respect to redshift $z$. To constrain the model parameters, we analyze various datasets including the $Hubble$, $Pantheon$ datasets, and their combination. Our results indicate that the Weyl-type $f(Q,T)$ theory offers a viable alternative to explain the observed late-time acceleration of the Universe avoiding the use of dark energy., Comment: Special Issue Celebrating the 20th Anniversary of IJGMMP

This paper explores the dark energy phenomenon within the context of $f(R,L_m)$ gravity theory. Two specific non-linear $f (R, L_m)$ models are considered: $f(R,L_m)=\frac{R}{2}+L_m^\alpha$ and $f(R,L_m)=\frac{R}{2}+(1+\alpha R)L_m$, where the parameter $\alpha$ is free. Here, we adopt a parametrization form for the Hubble parameter in terms of redshift $z$ as $H(z)=H_0 \left[A(1+z)^3+B+\epsilon \log(1+z)\right]^\frac{1}{2}$, which allows for deviations from the standard $\Lambda$CDM model at both low and high redshifts. We then incorporate the Hubble parameter solution into the Friedmann equations for both models. We employ Bayesian analysis to estimate the constraints on the free parameters $H_0$, $A$, $B$, and $\epsilon$ using the Hubble measurements and the Pantheon dataset. Further, we investigate the evolution of key cosmological quantities, such as the deceleration parameter, energy density, pressure, EoS parameter, and energy conditions. The evolution of the deceleration parameter reveals a significant transition from a decelerating phase to an accelerating phase in the Universe. The EoS parameter exhibits quintessence-like behavior for both non-linear $f (R, L_m)$ models., Comment: Physics of Dark Universe accepted version

We propose a novel approach to parameterize the equation of state for Scalar Field Dark Energy (SFDE) and use it to derive analytical solutions for various cosmological parameters. Using statistical MCMC with Bayesian techniques, we obtain constraint values for the model parameters and analyze three observational datasets. We find a quintessence-like behavior for Dark Energy (DE) with positive values for both model parameters $\alpha$ and $\beta$. Our analysis of the $CC$+$BAO$+$SNe$ datasets reveals that the transition redshift and the current value of the deceleration parameter are $z_{tr}=0.73_{-0.01}^{+0.03}$ and $q_{0}=-0.44_{-0.02}^{+0.03}$, respectively. We also investigate the fluid flow of accretion SFDE around a Black Hole (BH) and analyze the nature of the BH's dynamical mass during accretion, taking into account Hawking radiation and BH evaporation. Our proposed model offers insight into the nature of DE in the Universe and the behavior of BHs during accretion., Comment: The European Physical Journal Plus accepted veriosn

This study proposes a novel parametrization approach for the dimensionless Hubble parameter i.e. $E^2(z)=A(z)+\beta (1+\gamma B(z))$ in the context of scalar field dark energy models. The parameterization is characterized by two functions, $A(z)$ and $B(z)$, carefully chosen to capture the behavior of the Hubble parameter at different redshifts. We explore the evolution of cosmological parameters, including the deceleration parameter, density parameter, and equation of state parameter. Observational data from Cosmic Chronometers (CC), Baryonic Acoustic Oscillations (BAO), and the Pantheon+ datasets are analyzed using MCMC methodology to determine model parameters. The results are compared with the standard $\Lambda$CDM model using the Planck observations. Our approach provides a model-independent exploration of dark energy, contributing to a comprehensive understanding of late-time cosmic acceleration., Comment: Results in Physics accepted version

This paper is a parametrization of the equation of state (EoS) parameter of dark energy (DE), which is parameterized using Square-Root (SR) form i.e. $\omega _{SR}=\text{$\omega _{0}$}+\text{$\omega _{1}$}\frac{z}{\sqrt{z^{2}+1}}$, where $\omega _{0}$ and $\omega _{1}$ are free constants. This parametrization will be examined in the context of the recently suggested $f(Q)$ gravity theory as an alternative to General Relativity (GR), in which gravitational effects are attributed to the non-metricity scalar $Q$ with the functional form $f(Q)=Q+\alpha Q^{n}$, where $\alpha$ and $n$ are arbitrary constants. We derived observational constraints on model parameters using the Hubble dataset with 31 data points and the Supernovae (SNe) dataset from the Pantheon samples compilation dataset with 1048 data points. For the current model, the evolution of the deceleration parameter, density parameter, EoS for DE, and $Om(z)$ diagnostic have all been investigated. It has been shown that the deceleration parameter favors the current accelerated expansion phase. It has also been shown that the EoS parameter for DE has a quintessence nature at this time., Comment: Communications in Theoretical Physics accepted version

Despite the significant accomplishments of general relativity, numerous unresolved issues persist in our understanding of the cosmos. One of the most perplexing challenges is the ongoing accelerated expansion of the Universe, which continues to elude a complete explanation. Consequently, scientists have proposed various alternative theories to GR in pursuit of a deeper understanding. In our analysis, we delve into the recently proposed modified $f(Q)$ gravity, where $Q$ represents the non-metricity scalar responsible for gravitational effects. Specifically, we investigate a cosmological model characterized by the functional form $f(Q) = Q+\alpha Q^n$, where $\alpha$ (with $\alpha \neq 0$) and $n$ serve as free parameters. Utilizing this functional form, we construct our Hubble rate, incorporating a specific equation of state to describe the cosmic fluid. Furthermore, we leverage a dataset consisting of 31 data points from Hubble measurements and an additional 1048 data points from the Pantheon dataset. These data serve as crucial constraints for our model parameters, and we employ the Markov Chain Monte Carlo (MCMC) method to explore the parameter space and derive meaningful results. With our parameter values constrained, our analysis yields several noteworthy findings. The deceleration parameter suggests a recent accelerated phase in the cosmic expansion. In addition, the EoS parameter paints a portrait of dark energy exhibiting phantom-like characteristics. Furthermore, we delve into the application of cosmological diagnostic tools, specifically the statefinder and the $Om(z)$ diagnostics. Both of these tools align with our previous conclusions, confirming the phantom-like behavior exhibited by our cosmological model. These results collectively contribute to our understanding of the dynamic interplay between gravity, dark energy, and the expanding cosmos., Comment: Progress of Theoretical and Experimental Physics accepted version

This study delves into modified gravity theories that are equivalent to General Relativity but involve the torsion or non-metricity scalar instead of the curvature scalar. Specifically, we focus on $f(Q,T)$ gravity, which entails an arbitrary function of the non-metricity scalar $Q$ non-minimally coupled to the trace of the stress-energy tensor $T$. We investigate the functional form $f(Q,T)=f(Q)+f(T)$, where $f(Q) =Q+\alpha\,Q^2$ represents the Starobinsky model in $f(Q)$ gravity and $f(T)=2\,\gamma\,T$, with $\alpha$ and $\gamma$ are constants. To obtain solutions for the Friedmann equations, we introduce the concept of a constant jerk and employ its definition to trace the evolution of other kinematic variables, including the deceleration parameter, energy density, EoS parameter, and various energy conditions. These analyses serve to validate the proposed model. We constrain our constant jerk model using the most available Pantheon set of data, the Hubble set of data, and the BAO set of data. Further, we employ $Om(z)$ diagnostic as a means to differentiate between different theories of dark energy. Throughout our examination, all cosmological parameters under scrutiny consistently indicate an accelerating Universe., Comment: Chinese Journal of Physics accepted version

Understanding the accelerating expansion of the Universe remains a fundamental challenge in modern cosmology. In this paper, we investigate a cosmological model parametrized by a generalized variable deceleration parameter to elucidate the dynamics driving cosmic acceleration. By employing constraints from the latest observational datasets, including Cosmic Chronometers (CC), Type Ia Supernovae (SNe), and Baryon Acoustic Oscillations (BAO), we assess the compatibility of the model with observational data. The chosen parametrization aligns with thermodynamic constraints on the deceleration parameter, further validating its reliability. Further, we estimate the present value of the Hubble parameter, transition redshift, deceleration parameter, and EoS parameter, which align with observational data. Lastly, our stability analysis confirms the model's stability against small perturbations., Comment: Physics of the Dark Universe accepted version

We conduct a Bayesian analysis of recent observational datasets, specifically the Cosmic Chronometers (CC) dataset and Pantheon samples, to investigate the evolution of the EoS parameter in dark energy models. Our study focused on the effective EoS parameter, which is described by the parametric form $\omega_{eff}=-\frac{1}{1+m(1+z)^n}$, where $m$ and $n$ are model parameters. This parametric form is applicable within the framework of $f(R,L_m)$ gravity, where $R$ represents the Ricci scalar and $L_m$ is the matter Lagrangian. Here, we examine a non-linear $f(R,L_m)$ model characterized by the functional form $f(R,L_m)=\frac{R}{2}+L_m^\alpha$, where $\alpha$ is the free parameter of the model. We examine the evolution of several cosmological parameters, including the effective EoS parameter $\omega_{eff}$, the deceleration parameter $q$, the density parameter $\rho$, the pressure $p$, and the statefinder parameters. Our analysis revealed that the constrained current value of the effective EoS parameter, $\omega_{eff}^{0}=-0.68\pm0.06$ for both the CC and Pantheon datasets, points towards a quintessence phase. Moreover, at redshift $z=0$, the deceleration parameter, $q_0 = -0.61^{+0.01}_{-0.01}$, indicates that the present Universe is undergoing accelerated expansion., Comment: The European Physical Journal Plus published version

We reconstruct the effective Equation of State (EoS) within the framework of General Relativity (GR) theory in a homogeneous and isotropic FLRW Universe, which is assumed to be composed of matter and Dark Energy (DE). Our analysis employs a dataset consisting of 31 Cosmic Chronometer (CC) data points, six data points of Baryon Acoustic Oscillations (BAO), and 1048 Type Ia Supernovae (SN) from the Pantheon sample, and we determine the best-fit values of the model parameters through Markov Chain Monte Carlo (MCMC) simulation. We then use these parameter values to calculate various cosmological parameters, such as the DE EoS parameter, the energy density, the deceleration parameter, the state finder parameters, and the $Om(z)$ diagnostic. All the analyzed cosmological parameters show behavior consistent with the accelerated Universe scenario., Comment: PTEP published version

In this study, we investigate the cosmological history within the framework of modified $f(Q)$ gravity, which proposes an alternative theory of gravity where the gravitational force is described by a non-metricity scalar. By employing a parametrization scheme for the Hubble parameter, we obtain the exact solution to the field equations in $f(Q)$ cosmology. To constrain our model, we utilize external datasets, including 57 data points from the Hubble dataset, 1048 data points from the SN dataset, and six data points from the BAO dataset. This enables us to determine the best-fit values for the model parameters involved in the parameterization scheme. We analyze the cosmic evolution of various cosmological parameters, including the deceleration parameter, which exhibits the expected behavior in late-time cosmology and changes its signature with redshift. Further, we present the evolution of energy density, EoS parameter, and other geometrical parameters with respect to redshift. Furthermore, we discuss several cosmological tests and diagnostic analyses. Our findings demonstrate that the late-time cosmic evolution can be adequately described without the need for dark energy by employing a parametrization scheme in modified gravity., Comment: Chinese Journal of Physics published version

In this paper, we consider a comprehensive investigation of the cosmological model described by $f(R,T) = R + 2\lambda T$ (where $\lambda$ represents a free parameter) in light of the most recent observational data. By constraining the model using $Hubble$ and $Pantheon$ datasets, we determine its compatibility with the observed behavior of the Universe. For this purpose, we adopt a parametric form for the effective equation of state (EoS) parameter. This parametric form allows us to describe the evolution of the EoS parameter with respect to redshift and investigate its behavior during different cosmic epochs. The analysis of the deceleration parameter reveals an accelerating Universe with a present value of $q_0=-0.64^{+0.03}_{-0.03}$, indicating the current phase of accelerated expansion. The transition redshift is found to be $z_{tr}=0.53^{+0.04}_{-0.03}$, marking the epoch of transition from deceleration to acceleration. We also analyze the evolution of important cosmological parameters including density parameter, pressure, effective EoS, and stability. These findings collectively demonstrate the viability of the $f(R,T)$ cosmological model as a robust candidate capable of engendering the requisite negative pressure, thereby efficiently propelling cosmic expansion. Moreover, the undertaken stability analysis underscores the model's stability within the broader cosmic landscape. By providing the best-fit values for the coupling parameter $\lambda$, this approach motivates and encourages further explorations into the extensive landscape of this model and its potential applications across diverse realms of cosmology and astronomy., Comment: CPC accepted version

In this paper, we focus on the parametrization of the effective equation of state (EoS) parameter within the framework of $f(Q)$ symmetric teleparallel gravity. Here, the gravitational action is represented by an arbitrary function of the non-metricity scalar $Q$. By utilizing a specific parametrization of the effective EoS parameter and a power-law model of $f(Q)$ theory, namely $f(Q)=\beta Q^{\left( m+1\right) }$ (where $\beta$ and $m$ are arbitrary constants), we derive the cosmological solution of the Hubble parameter $H(z)$. To constrain model parameters, we employ recent observational data, including the Observational Hubble parameter Data ($OHD$), Baryon Acoustic Oscillations data ($BAO$), and Type Ia supernovae data ($SNe$ Ia). The current constrained value of the deceleration parameter is found to be $q_{0}=-0.50^{+0.01}_{-0.01}$, indicating that the current Universe is accelerating. Furthermore, we examine the evolution of the density, EoS, and $Om(z)$ diagnostic parameters to deduce the accelerating nature of the Universe. Finally, we perform a stability analysis with linear perturbations to confirm the model's stability., Comment: Physics of the Dark Universe published version

We present a new $f(Q)$ cosmological model capable of reproducing late-time acceleration, i.e. $f\left( Q\right) = \lambda_{0}\left( \lambda +Q\right) ^{n}$ by supporting certain parametrization of the Hubble parameter. By using observational data from Hubble, Pantheon, and Baryonic Acoustic Oscillations (BAO) dataset, we investigate the constraints on the proposed quadratic Hubble parameter $H(z)$. This proposal caused the Universe to transition from its decelerated phase to its accelerated phase. Further, the current constrained value of the deceleration parameter from the combined Hubble+Pantheon+BAO dataset is $q_{0}=-0.285\pm 0.021$, which indicates that the Universe is accelerating. We also analyze the evolution of energy density, pressure, and EoS parameters to infer the Universe's accelerating behavior. Finally, we use a stability analysis with linear perturbations to assure the model's stability., Comment: Physics of the Dark Universe published version

We propose a logarithmic parametrization form of energy density for the scalar field dark energy in the framework of the standard theory of gravity, which supports the necessary transition from the decelerated to the accelerated behavior of the Universe. The model under consideration is constrained by available observational data, including cosmic chronometers data-sets (CC), Baryonic Acoustic Oscillation (BAO) data-sets, and Supernovae (SN) data-sets, consisting of only two parameters $\alpha$ and $\beta$. The combined $CC$+$BAO$+$SN$ data-sets yields a transition redshift of $z_{tr}=0.79^{+0.02}_{-0.02}$, where the model exhibits signature-flipping and is consistent with recent observations. For the combined data-sets, the present value of the deceleration parameter is calculated to be $q_{0}=-0.43^{+0.06}_{-0.06}$. Furthermore, the analysis yields constraints on both the parameter density value for matter and the present value of the Hubble parameter, with values of $\Omega_{m0}=0.25849^{+0.00026}_{-0.00025}$ and $H_{0}=67.79_{-0.59}^{+0.59}$ $km/s/Mpc$, respectively, consistent with the results obtained from Planck 2018. Finally, the study investigates how the mass of a black hole evolves over time in a Universe with both matter and dark energy. It reveals that the black hole mass increases initially but stops increasing as dark energy dominates., Comment: The European Physical Journal C published version

In this paper, we propose a new parametrization of dark energy based on the $Om(z)$ diagnostic tool behavior. For this purpose, we investigate a functional form of the $Om(z)$ that predicts the popular dark energy dynamical models, namely phantom and quintessence. We also found the famous cosmological constant for specified values of the model's parameters. We employed the Markov Chain Monte Carlo approach to constrain the cosmological model using Hubble, Pantheon samples, and BAO datasets. Finally, we used observational constraints to investigate the characteristics of dark energy evolution and compare our findings to cosmological predictions., Comment: The European Physical Journal C accepted version

The problem of cosmic acceleration and dark energy is one of the mysteries presently posed in the scientific society that general relativity has not been able to solve. In this work, we have considered alternative models to explain this late-time acceleration in a flat Friedmann-Lema\^i% tre-Robertson-Walker (FLRW) Universe within the framework of the $% f\left(Q,T\right) $\ modified gravity theory (where $Q$ is the non-metricity and $T$ is the trace of the energy-momentum tensor) recently proposed by Xu et al. (Eur. Phys. J. C 79 (2019) 708), which is an extension of $f\left( Q\right) $ gravity with the addition of the $T$ term. Here, we presume a specific form of $f\left( Q,T\right) =\alpha Q+\beta Q^{2}+\gamma T$ where $% \alpha $, $\beta $ and $\gamma $ are free model parameters, and obtained the exact solutions by assuming the cosmic time-redshift relation as $t(z)=\frac{% nt_{0}}{m}g(z)$ which produces the Hubble parameter of the form $H(z)=\frac{% mH_{0}}{m+n}\left[ \frac{1}{g(z)}+1\right] $ where $m$ and $n$ are the non-negative constants, we find the best values for them using 57 data points of the Hubble parameter $H\left( z\right) $. Also, we find the behavior of different cosmological parameters as the deceleration parameter $% \left( q\right) $, energy density $\left( \rho \right) $, pressure $% \left(p\right) $ and EoS parameter $\left( \omega \right) $ and compare them with the observational results. To ensure the validity of the results, we studied the energy conditions along with jerk parameter. Finally, we find that our model behaves similarly to the quintessence Universe., Comment: IJMPD accepted version

This study investigates the dynamics of a spatially homogeneous and anisotropic LRS Bianchi type-I universe with viscous fluid in the framework of $f(Q)$ symmetric teleparallel gravity. We assume a linear form for $f(Q)$ and introduce hypotheses regarding the relationship between the expansion and shear scalars, as well as the Hubble parameter and bulk viscous coefficient. The model is constrained using three observational datasets: the Hubble dataset (31 data points), the Pantheon SN dataset (1048 data points), and the BAO dataset (6 data points). The calculated cosmological parameters indicate expected behavior for matter-energy density and bulk viscous pressure, supporting the universe's accelerating expansion. Diagnostic tests suggest that the model aligns with a $\Lambda$CDM model in the far future and resides in the quintessence region. These findings are consistent with recent observational data and contribute to our understanding of cosmic evolution within the context of modified gravity and bulk viscosity., Comment: Modern Physics Letters A accepted version

In this paper we review the Myrzakulov Gravity models (MG-N, with $\mathrm{N = I, II, \ldots, VIII}$) and derive their respective metric-affine generalizations (MAMG-N), discussing also their particular sub-cases. The field equations of the theories are obtained by regarding the metric tensor and the general affine connection as independent variables. We then focus on the case in which the function characterizing the aforementioned metric-affine models is linear and consider a Friedmann-Lema\^{i}tre-Robertson-Walker background to study cosmological aspects and applications., Comment: 45 pages

Symmetric Teleparallel Gravity is an exceptional theory of gravity that is consistent with the vanishing affine connection. This theory is an alternative and a simpler geometrical formulation of general relativity, where the non-metricity $Q$ drives the gravitational interaction. Our interest lies in exploring the cosmological bouncing scenarios in a flat Friedmann-Lima\^itre-Robertson-Walker (FLRW) spacetime within this framework. We explore bouncing scenarios with two different Lagrangian forms of $f(Q)$ such as a linearly and non-linearly dependence on $Q$. We have successfully examined all the energy conditions and stability analysis for both models to present a matter bounce., Comment: Revision submitted EPJP

In this paper, we consider some metric-affine Myrzakulov gravity (MG) theories with Gauss-Bonnet scalars. Also we consider the MG theories with the boundary term scalars. Note that these MG theories with the Gauss-Bonnet and boundary term scalars were proposed in [arXiv:1205.5266]. Some examples of Metric-Affine Gravity (MAG) theories are reviewed in the context of the $F(R,T,Q,{\cal T}, {\cal D})$ type models. Then the generalized MAG theory with the curvature, torsion and nonmetricity (the so-called MG-VIII) was studied. For the FRW spacetime case, in particular, the Lagrangian, Hamilatonian and gravitational equations are obtained. The particular case $F(R,T)=\alpha R+\beta T+\mu Q+\nu{\cal T}$ is investigated in detail. In quantum case, the corresponding Wheeler-DeWitt equation is obtained. Finally, some gravity theories with the curvature, torsion and nonmetricity are presented., Comment: 41 pages. arXiv admin note: substantial text overlap with arXiv:1205.5266

In this paper, we obtained a class of oscillatory, cyclic and knot type solutions from the non-linear Friedmann equations. This is performed by choosing specific forms of energy density and pressure of matter. All the expressions written here are in dimensionless form. We show that evolutionary path taken by the spatial coordinates in the model follow various knots, specifically trefoil and eight-knots. We provide several examples and plot relevant cosmological parameters in figures. Our cyclic models can be interpreted as a periodic cosmological model, such that early and late time acceleration are unified under the same mechanism., Comment: 13 pages, 6 figures, revised exposition, typos corrected, results unchanged