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In this study, we explored late-time cosmology within an extended class of theories based on $f(Q, L_m)$ gravity. This theory generalizes $f(Q)$ gravity by incorporating a non-minimal coupling between the non-metricity $Q$ and the matter Lagrangian $L_m$, analogous to the $f(Q,T)$ theory. The coupling between $Q$ and $L_m$ leads to the non-conservation of the matter energy-momentum tensor. We first investigated a cosmological model defined by the functional form $f(Q, L_m) = \alpha Q + \beta L_m^n$, where $\alpha$, $\beta$, and $n$ are constants. The derived Hubble parameter $H(z) = H_0 (1+z)^{\frac{3n}{2(2n-1)}}$ indicates that $n$ significantly influences the scaling of $H(z)$ over cosmic history, with $n > 2$ suggesting accelerated expansion. We also examined the simplified case of $n = 1$, leading to the linear form $f(Q, L_m) = \alpha Q + \beta L_m$, consistent with a universe dominated by non-relativistic matter. Using various observational datasets, including $H(z)$ and Pantheon, we constrained the model parameters. Our analysis showed that the $f(Q, L_m)$ model aligns well with observational results and exhibits similar behavior to the $\Lambda$CDM model. The results, with $q_0 = -0.22 \pm 0.01$ across all datasets, indicate an accelerating universe, highlighting the model's potential as an alternative to $\Lambda$CDM., Comment: Journal of High Energy Astrophysics accepted version

Motivated by anomalies in cosmic microwave background observations, we investigate the implications of $f(Q, T)$ gravity in Bianchi type-I spacetime, aiming to characterize the universe's spatially homogeneous and anisotropic properties. By using a linear combination of non-metricity $Q$ and the energy-momentum tensor trace $T$, we parametrize the deceleration parameter and derive the Hubble solution, which we then impose in the Friedmann equations of $f(Q, T)$ gravity. Bayesian analysis is employed to find the best-fit values of model parameters, with $1-\sigma$ and $2-\sigma$ contour plots illustrating the constraints from observational data, including $H(z)$ data and the Pantheon+ sample. Our analysis reveals a transition from a decelerated to an accelerated expansion phase, with the present deceleration parameter indicating an accelerating universe. The energy density gradually decreases over time, approaching zero for the present and future, indicating continuous expansion. The anisotropic pressure, initially notably negative, transitions to slightly negative values, suggesting the presence of dark energy. The evolving equation of state parameter $\omega$ exhibits behavior akin to phantom energy, influenced by spacetime anisotropy. Violations of the null energy condition and the strong energy condition imply phantom-like behavior and accelerated expansion., Comment: Journal of High Energy Astrophysics accepted version

This study explores the extension of teleparallel gravity within the framework of general relativity, introducing an algebraic function $f(T)$ dependent on the torsion scalar $T$. Motivated by the teleparallel formulation, we investigate cosmological implications, employing the simplest parametrization of the dark energy equation of state. Our chosen $f(T)$ function, $f(T)=\alpha(-T)^n$, undergoes stringent constraints using recent observational data ($H(z)$, SNeIa, BAO, and CMB). The model aligns well with cosmic dynamics, exhibiting quintessence behavior. The evolution of the deceleration parameter, the behavior of dark energy components, and the $Om(z)$ diagnostic further reveal intriguing cosmological phenomena, emphasizing the model's compatibility with quintessence scenarios., Comment: Physics of the Dark Universe accepted version

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 this study, we examined the late-time cosmic expansion of the universe within the framework of $f(Q, L_m)$ gravity, where $Q$ denotes the non-metricity and $L_{m}$ represents the matter Lagrangian. We analyzed a linear $f(Q, L_m)$ model of the form $f(Q, L_m) = -\alpha Q + 2 L_{m} + \beta$. Using MCMC methods, we constrained the model parameters $H_0$, $\alpha$, and $\beta$ with various datasets, including $H(z)$, Pantheon+SH0ES, and BAO data. For the $H(z)$ dataset, we found $H_0 = 67.90 \pm 0.66$, $\alpha = 0.1072_{-0.0069}^{+0.0054}$, and $\beta = -1988.2 \pm 1.0$. For the Pantheon+SH0ES dataset, $H_0 = 70.05 \pm 0.68$, $\alpha = 0.0916_{-0.0033}^{+0.0028}$, and $\beta = -1988.3 \pm 1.0$. For the BAO dataset, $H_0 = 68.1 \pm 1.0$, $\alpha = 0.1029_{-0.0052}^{+0.0041}$, and $\beta = -1988.24 \pm 0.99$. Moreover, the energy density remains positive and approaches zero in the distant future, and the deceleration parameter indicates a transition from deceleration to acceleration, with transition redshifts of $z_t = 0.60$, $z_t = 0.78$, and $z_t = 0.66$ for the respective datasets. These findings align with previous observational studies and contribute to our understanding of the universe's expansion dynamics., Comment: Physics of the Dark Universe accepted version

In this paper, we investigate a cosmological model based on viscous $f(R,T)$ gravity as a potential alternative to dark energy. This model incorporates bulk viscosity and is analyzed using an effective equation of state. We consider the simplest specific model, $f(R,T)=R+\lambda T$, where $\lambda$ is a constant. The exact solution of our viscous $f(R,T)$ cosmological model is derived, and then we use the combined datasets consisting of 31 $H(z)$ data points and 1701 Pantheon+ SNe data points to determine the best-fit values of the model parameters. We find good agreement with observations, particularly at higher redshifts. Our model's behavior, including energy density, pressure with viscosity, effective equation of state, and deceleration parameter, is analyzed. It indicates a shift from decelerated to accelerated phases of the universe's expansion, suggesting that bulk viscosity in the cosmic fluid could effectively generate the negative pressure necessary for cosmic expansion. Finally, we explore statefinder diagnostics to differentiate between various dark energy models, revealing that our model resides in the quintessence region., Comment: Physics of the Dark Universe published version

We investigate the influence of bulk viscosity on late-time cosmic acceleration within an extended $f(Q, L_m)$ gravity framework, where the non-metricity $Q$ is non-minimally coupled with the matter Lagrangian $L_m$. Analyzing the function $f(Q, L_m) = \alpha Q + \beta L_m$, we derive exact solutions under non-relativistic matter domination. Using observational datasets ($H(z)$, Pantheon supernovae, and their combination), we constrain the model parameters $H_0$, $\alpha$, $\beta$, and $\zeta$. The deceleration parameter transitions from positive to negative values around redshifts $z_t \approx 0.80$ to $0.99 $, indicating current accelerated expansion. Moreover, the effective equation of state parameter, $\omega_{eff}$, resembles quintessence dark energy ($-1 < \omega_{eff} < -\frac{1}{3}$), with corresponding values from respective datasets. Finally, we use the $Om(z)$ diagnostic, which confirms that our model demonstrates quintessence-like behavior. Our findings underscore the significant role of bulk viscosity in understanding accelerated expansion in the universe within alternative gravity theories., Comment: 12 pages, 8 figures

In this study, we investigate signature flips within the framework of cosmological models featuring a time-varying vacuum energy term $\Lambda(t)$. Specifically, we consider the power-law form of $\Lambda=\alpha H^n$, where $\alpha$ and $n$ are constants. To constrain the model parameters, we use the MCMC technique, allowing for effective exploration of the model's parameters. We apply this approach to analyze 31 points of observational Hubble Data (OHD), 1048 points from the Pantheon data, and additional CMB data. We consider three scenarios: when $n$ is a free parameter (Case I), when $n=0$ (Case II), and when $n=1$ (Case III). In our analysis across all three cases, we observe that our model portrays the universe's evolution from a matter-dominated decelerated epoch to an accelerated epoch, as indicated by the corresponding deceleration parameter. In addition, we investigate the physical behavior of total energy density, total EoS parameter, and jerk parameter. Our findings consistently indicate that all cosmological parameters predict an accelerated expansion phase of the universe for all three cases ($q_0<0$, $\omega_0<-\frac{1}{3}$, $j_0>0$). Furthermore, our analysis reveals that the $Om(z)$ diagnostics for Cases I and III align with the quintessence region, while Case II corresponds to the $\Lambda$CDM model., Comment: The European Physical Journal C published version

In this work, we investigate the dynamics of bouncing cosmologies within the framework of Weyl-type $f(Q,T)$ gravity. Here, $Q$ represents the non-metricity of the space-time, is determined by the vector field $w_\mu$, while $T$ represents the trace of the matter energy-momentum tensor. Our objective is to explore the feasibility of avoiding the Big Bang singularity by implementing a matter-bounce cosmology. To achieve this, we consider a specific model with the functional form $f(Q,T)=\alpha Q+\frac{\beta }{6\kappa ^2}T$, where $\alpha$ and $\beta$ are model parameters. We analyze the dynamical parameters associated with this model and examine the influence of the Weyl-type $f(Q,T)$ theory on these parameters. Moreover, we assess the stability of the proposed model to ensure its viability as a cosmological scenario. Through our analysis, we aim to gain insights into the potential implications and consequences of Weyl-type $f(Q,T)$ gravity for bouncing scenarios, contributing to our understanding of alternative gravitational theories in the context of cosmology., Comment: Chinese Journal of Physics published version

Understanding the evolution of dark energy poses a significant challenge in modern cosmology, as it is responsible for the universe's accelerated expansion. In this study, we focus on a specific $f(T)$ cosmological model and analyze its behavior using observational data, including 31 data points from the CC dataset, 1048 points from the Pantheon SNe Ia samples, and 6 points from the BAO dataset. By considering a linear $f(T)$ model with an additional constant term, we derive the expression for the Hubble parameter as a function of cosmic redshift for non-relativistic pressureless matter. We obtain the best-fit values for the Hubble constant, $H_0$, and the model parameters $\alpha$ and $\beta$, indicating a stable model capable of explaining late-time cosmic acceleration without invoking a dark energy component. This is achieved through modifying field equations to account for the observed accelerated expansion of the universe., Comment: Physics of the Dark Universe published version

In this study, we investigate the role of bulk viscosity in $f(Q,T)$ gravity in explaining late-time cosmic acceleration. This model, an extension of symmetric teleparallel gravity, introduces viscosity into cosmic matter dynamics for a more realistic representation. Specifically, we consider the linear form of $f (Q, T) =\alpha Q + \beta T$, where $\alpha$ and $\beta$ are free model parameters. To assess the model, we derive its exact solution and use Hubble parameter $H(z)$ data and Pantheon + SNe Ia data for parameter estimation. We employ the $\chi^2$ minimization technique alongside the MCMC random sampling method to determine the best-fit parameters. Then, we analyze the behavior of key cosmological parameters, including the deceleration parameter, bulk viscous matter-dominated universe density, effective pressure, and the effective EoS parameter, accounting for the viscous type fluid. We observe a transition in the deceleration parameter from a positive (decelerating) to a negative (accelerating) phase at transition redshift $z_t$. The matter density shows the expected positive behavior, while the pressure, influenced by viscosity, exhibits negative behavior, indicative of accelerating expansion. Furthermore, we investigate the energy conditions and find that while the NEC and DEC meet positivity criteria, the SEC is violated in the present and future epochs. The $Om(z)$ diagnostic suggests that our model aligns with quintessence behavior. Finally, our $f(Q,T)$ cosmological model, incorporating bulk viscosity effects, provides a compelling explanation for late-time cosmic behavior, consistent with observational data., Comment: Physics of the Dark Universe accepted version

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

In this paper, we present an accelerating cosmological model by constraining the free parameters using the cosmological datasets in an extended symmetric teleparallel gravity for the flat and anisotropic space-time. We employ a time variable deceleration parameter that behaves early deceleration and late time acceleration in the form of Hybrid Scale Factor (HSF). We obtain the present values of deceleration parameter and analyse the late time behavior of the Universe based on the best-fit values of free parameters. We derive the dynamical parameters of the model and obtain the equation of state parameter at present in the quintessence region; however at late time it approaches to $\Lambda$CDM. The energy conditions are also analysed to validate the modified gravity and we find that strong energy condition is violating. We establish the importance of hybrid scale factor in the late time cosmic phenomena issue., Comment: Annalen Der Physik published version

This paper explores the impact of the Yang-Mills charge parameter and the exponent term on a $4$D black hole solution in the Einstein Power-Yang-Mills theory. Through an investigation of the massless scalar quasinormal mode spectrum, black hole shadow, and emission rate, we have determined that the effects of these two parameters are opposite. Specifically, the Yang-Mills charge parameter causes an increase in the real quasinormal frequencies with a correspondingly smaller damping rate. It also results in a smaller black hole shadow and a lower evaporation rate., Comment: 13 pages, 9 figures

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

In this paper, we have presented an accelerating cosmological model of the Universe in an extended symmetric teleparallel gravity or $f(Q,T)$ gravity. The parametric form of the Hubble parameter is, $H\left(z\right) =H_{0}\left[ \alpha +\left( 1-\alpha \right) \left( 1+z\right) ^{n}\right] ^{\frac{3}{2n}}$, where $H_0$ and $n$ are constants and for $n=3$, the $\Lambda$CDM scenario can be obtained. We have considered the logarithmic form of $f(Q,T)$ as, $f(Q,T)=-Q+\beta \log\left(\frac{Q}{Q_{0}}\right)+\gamma T$, where $\beta $ and $\gamma $ are the free model parameters. Using the Hubble, Baryon Acoustic Oscillations (BAO), and Type Ia Supernovae (SNe Ia) datasets, the present value of the Hubble parameter and other free parameters are constrained. Further other cosmographic and dynamical parameters are presented using the obtained constrained values of the Hubble and free parameters. The model shows the quintessence behavior of the Universe at the present time. The present value of the EoS parameter is obtained as, $\omega_{0}=-0.56$ for the $Hubble+BAO+SNe$ datasets. The energy conditions are presented and the violation of the strong energy condition has been shown. We have performed the dynamical system analysis to validate the stability of the model. From the evolutionary plot obtained through the dynamical system variables, the present value of density parameters have been obtained as $\Omega_m\approx0.3$ and $\Omega_{de}\approx0.7$., Comment: Nuclear Physics B published version

In the past few years, $f(Q)$ theories have drawn a lot of research attention in replacing Einstein's theory of gravity successfully. The current study examines the novel cosmological possibilities emerging from two specific classes of $f(Q)$ models using the parametrization form of the equation of state (EoS) parameter as $\omega \left( z\right) =-\frac{1}{1+3\beta \left( 1+z\right) ^{3}}$, which displays quintessence behavior with the evolution of the Universe. We do statistical analyses using the Markov chain Monte Carlo (MCMC) method and background datasets like Type Ia Supernovae (SNe Ia) luminosities and direct Hubble datasets (from cosmic clocks), and Baryon Acoustic Oscillations (BAO) datasets. This lets us compare these new ideas about the Universe to the $\Lambda $CDM model in a number of different possible ways. We have come to the conclusion that, at the current level of accuracy, the values of their specific parameters are the best fits for our $f(Q)$ models. To conclude the accelerating behavior of the Universe, we further study the evolution of energy density, pressure, and deceleration parameter for these $f(Q)$ models., Comment: EPJC accepted 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

On the basis of homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) geometry, solutions to the issues of cosmic acceleration and dark energy are being put forth within the context of $f\left( Q\right)$ gravity. We take into account a power law $f(Q)$ model using $f\left( Q\right) =\alpha Q^{n}$, where $\alpha $ and $n$ are free model parameters. In the current scenario, we may establish the energy density and pressure for our $f(Q)$ cosmic model by applying the constant sound speed parameterizations, i.e., $\vartheta_{s}^{2}=\beta$, where a barotropic cosmic fluid is described in terms of $\beta$. The field equations are then derived, and their precise solutions are established. We obtain the constraints on the model parameters using the updated Hubble (Hz) data sets consisting of 31 data points, the recently published Pantheon samples (SNe) with 1048 points, and Baryon acoustic oscillations (BAO) data sets. We also examine the physical behaviour of the deceleration parameter, the equation of state (EoS) parameter, the statefinder diagnostic, and the Om diagnostic. We conclude that our $f\left( Q\right) $\ cosmic model predicts a transition in the universe from deceleration to acceleration. Further, to investigate the feasibility of the model, we discussed some of its thermodynamic aspects., Comment: Nuclear Physics B published version

$f(Q,T)$ theory of gravity is very recently proposed to incorporate within the action Lagrangian, the trace $T$ of the energy-momentum tensor along with the non-metricity scalar $Q$. The cosmological application of this theory in a spatially flat isotropic and homogeneous Universe is well-studied. However, our Universe is not isotropic since the Planck era and therefore to study a complete evolution of the Universe we must investigate the $f(Q,T)$ theory in a model with a small anisotropy. This motivated us to presume a locally rotationally symmetric (LRS) Bianchi-I spacetime and derive the motion equations. We analyse the model candidate $f(Q,T)=\alpha Q^{n+1}+\beta T$, and to constrain the parameter $n$, we employ the statistical Markov chain Monte Carlo (MCMC) method with the Bayesian approach using two independent observational datasets, namely, the Hubble datasets, and Type Ia supernovae (SNe Ia) datasets., Comment: AOP accepted version

In this work, we have studied the quasinormal modes of a black hole in a model of the type $f(Q)=\underset{n}{\sum}a_{n}\left(Q-Q_{0}\right)^{n} $ in $f(Q)$ gravity by using a recently introduced method known as Bernstein spectral method and confirmed the validity of the method with the help of well known Pad\'e averaged higher order WKB approximation method. Here we have considered scalar perturbation and electromagnetic perturbation in the black hole spacetime and obtained the corresponding quasinormal modes. We see that for a non-vanishing nonmetricity scalar $Q_0$, quasinormal frequencies in scalar perturbation are greater than those in electromagnetic perturbation scenarios. On the other hand, the damping rate of gravitational waves is higher for electromagnetic perturbation. To confirm the quasinormal mode behaviour, we have also investigated the time domain profiles for both types of perturbations., Comment: 15 pages, 6 figures. 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

We investigate the history of the cosmos using an extension of symmetric teleparallel gravity, namely Weyl-type $f(Q,T)$ gravity, where $Q$ represents the non-metricity scalar of space-time in the standard Weyl form, completely specified by the Weyl vector $w_{\mu }$, and $T$ represents the trace of the matter energy-momentum tensor. We derive the Hubble parameter from the proposed form of the time-dependent deceleration parameter $q=A-% \frac{B}{H^{2}}$, where $A$ and $B$ are free constants and then use a model-independent method to apply it to the Friedmann equations of Weyl-type $f(Q,T)$ gravity. Further, we determine the best fit values of the model parameters using new Hubble sets of data of 31 points and Type Ia Supernovae (SNe Ia) sets of data of 1048 points. Finally, we examine the behavior of the effective equation of state~(EoS)~parameter and we observe that the best fit values of the model parameters supports a crossing of the phantom divide line i.e. $\omega _{eff}=-1$ from $\omega _{eff}>-1$ (quintessence phase) to $\omega _{eff}<-1$ (phantom phase). According to the current study, Weyl-type $f(Q,T)$ gravity can give an alternative to dark energy (DE) in solving the existing cosmic acceleration., Comment: Submitted to CJPHY

In this study, we investigate the consequence of the constant-roll condition and examine the role of $f(Q,T)$ gravity in the cosmological inflation process. We analyze the inflationary scenario by calculating modified Friedmann equations, and giving an alternative technique that enables relating modified slow-roll parameters to the constant roll parameter $\beta $. Considering both chaotic and hilltop models, we calculate the spectral index and the tensor-to-scalar ratio and compare their compatibility with Planck's data for different choices of the constant roll parameter $\beta $. We examine the evolution of primordial black holes in our chosen modified gravity model taking into account the accretion process and the evaporation due to Hawking radiation. We compute the evaporation and accretion masses rate and provide an analytic estimation of the primordial black holes masse and of the radiation in the $f(Q,T)$ gravity model., Comment: 18 pages, 5 figures

In this paper, we investigate the existence of bulk viscous FLRW cosmological models in a recently proposed extended symmetric teleparallel gravity or $f\left( Q,T\right) $ gravity in which $Q$ is the non-metricity and $T$ is the trace of the energy-momentum tensor. We consider a simple coupling between matter and non-metricity, specifically, $f\left( Q,T\right) =\alpha Q^{m+1}+\lambda T$ and $f\left( Q,T\right) =\alpha Q+\lambda T$ where $\alpha $, $\lambda $ and $m$ are free model parameters. The exact cosmological solutions are found by assuming the scale factor in the form of the hybrid expansion law. This type of relation generates a time-varying deceleration parameter with the transition of the Universe from the early decelerating phase to the present accelerating phase. In the presence of viscous fluid, we analyze some cosmological parameters of our cosmological model such as the energy density, bulk viscous pressure, bulk viscous coefficient, equation of state parameter, and energy conditions. Finally, we conclude our $f\left( Q,T\right) $\ cosmological models agree with the recent astronomical observations., Comment: CJPHY accepted version

In Einstein's General Relativity (GR), the gravitational interactions are described by the spacetime curvature. Recently, other alternative geometric formulations and representations of GR have emerged in which the gravitational interactions are described by the so-called torsion or non-metricity. Here, we consider the recently proposed modified symmetric teleparallel theory of gravity or $f\left( Q\right) $ gravity, where $Q$ represents the non-metricity scalar. In this paper, motivated by several papers in the literature, we assume the power-law form of the function $% f\left( Q\right) $ as $f\left( Q\right) =\alpha Q^{n+1}+\beta $ (where $% \alpha $, $\beta $, and $n$ are free model parameters) that contains two models: Linear ($n=0$) and nonlinear ($n\neq 0$). Further, to add constraints to the field equations we assume the deceleration parameter form as a divergence-free parametrization. Then, we discuss the behavior of various cosmographic and cosmological parameters such as the jerk, snap, lerk, $Om$ diagnostic, cosmic energy density, isotropic pressure, and equation of state (EoS) parameter with a check of the violation of the strong energy condition (SEC) to obtain the acceleration phase of the Universe. Hence, we conclude that our cosmological $f(Q)$ models behave like quintessence dark energy (DE)., Comment: Submitted to IJGMMP

We discuss a spatially homogeneous and anisotropic Bianchi type-I space-time with two fluids as the content of the Universe: matter and holographic dark energy in the framework of general relativity. To get the exact solutions of Einstein's field equations, we choose the scale factor as a hyperbolic function, specifically, $a\left( t\right) =\sinh ^{\frac{1}{n}}\left( \gamma t\right) $, where $\gamma $ and $n>0$ are arbitrary constants, which gives us a time-dependent deceleration parameter. Then we study our cosmological model under the conditions of the parameters as: $\gamma $ fixed and $n>1$. Our cosmological solutions led to an early deceleration phase followed by the current observed acceleration phase. Further, the anisotropic parameter and some other physical parameters are discussed. We conclude that our cosmological model is consistent with the results of recent astronomical observations., Comment: JOAA accepted version

In this paper, we have examined the recently proposed modified symmetric teleparallel gravity, in which gravitational Lagrangian is given by an arbitrary function of non-metricity scalar $Q$. We have considered a constant jerk parameter to express the Hubble rate. Moreover, we have used 31 points of OHD datasets and 1701 points of Pantheon+ datasets to constraint our model parameters by means of the Markov Chain Monte Carlo analysis. The mean values and the best fit obtained give a consistent Hubble rate and deceleration parameter compared to the observation values. In order to study the current accelerated expansion scenario of the Universe with the presence of the cosmological fluid as a perfect fluid, we have considered two forms of teleparallel gravity. We have studied the obtained field equations with the proposed forms of $f(Q)$ models, specifically, linear $f\left( Q\right) =\alpha Q+\beta $ and non-linear $f\left( Q\right) =Q+mQ^{n}$ models. Next, we have discussed the physical behavior of cosmological parameters such as energy density, pressure, EoS parameter, and deceleration parameter for both model. To ensure the validity of our proposed cosmological models, we have checked all energy conditions. The properties of these parameters confirm that our models describe the current acceleration of the expansion of the Universe. This result is also corroborated by the energy conditions criteria. the Finally, the EoS parameter for both models indicates that the cosmological fluid behaves like a quintessence dark energy model., Comment: EPJ Plus 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

The paper presents Barrow holographic dark energy (infrared cut-off is the Hubble horizon) suggested by Barrow recently (Physics Letters B 808 (2020): 135643) in an anisotropic Bianchi type-I Universe within the framework of $% f\left( Q\right) $ symmetric teleparallel gravity, where the non-metricity scalar $Q$ is responsible for the gravitational interaction. We consider two cases: Interacting and non-interacting models of pressureless dark matter and Barrow holographic dark energy by solving $f\left( Q\right) $ symmetric teleparallel field equations. To find the exact solutions of the field equations, we assume that the time-redshift relation follows a Lambert function distribution as $t\left( z\right) =\frac{mt_{0}}{l}g\left( z\right) $, where $g\left( z\right) =LambertW\left[ \frac{l}{m}e^{\frac{l-\ln \left( 1+z\right) }{m}}\right] $, $m$ and $l$ are non-negative constants and $t_{0}$ represents the age of the Universe. Moreover, we discuss several cosmological parameters such as energy density, equation of state (EoS) and skewness parameters, squared sound speed, and $(\omega _{B}-\omega _{B}^{^{\prime }})$ plane. Finally, we found the values of the deceleration parameter (DP) for the Lambert function distribution as $q_{(z=0)}=-0.45$ and $q_{(z=-1)}=-1$ which are consistent with recent observational data, i.e. DP evolves with cosmic time from initial deceleration to late-time acceleration., Comment: IJGMMP accepted version

In this paper, we investigate the exact solution of an anisotropic space-time in the context of $f(Q)$ gravity, where $f\left( Q\right) $ is the arbitrary function of the non-metricity scalar $Q$. Here, we consider a specific power-law form as $f\left( Q\right) =\alpha Q^{n+1}+\beta $, where $\alpha $, $\beta $, and $n$ are free model parameters. Using power-law cosmology ($a\left( t\right) \propto t^{m}$), we analyze the physical behavior of cosmological parameters such as the energy density, pressure, EoS parameter, skewness parameter. Further, we validated the model with energy conditions and found that our $f\left( Q\right) $\ cosmological model behaves like the quintessence model in the present and $% \Lambda $CDM in the future., Comment: Minor revision in CJPHY. arXiv admin note: text overlap with arXiv:2208.08877