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In the present paper, we investigate constrained transit cosmological models in the most recent proposed modified gravity theory, $f(R,L_{m},T)$-gravity. We obtain the modified field equations for a flat homogeneous and isotropic Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) spacetime metric. We constrain the equation of continuity by imposing the equation of state for the perfect fluid source $p=-\frac{1}{3}\rho+p_{0}$ so that we get energy conservation equation as $\dot{\rho}+3H(\rho+p)=0$, (because generally, energy conservation law is not satisfied in $f(R,L_{m},T)$-gravity). Using this constraint, we establish a relation between the energy density parameters $\Omega_{m0}$, $\Omega_{r0}$, and $\Omega_{f0}$ and the Hubble function. After that, we made observational constraints on $H(z)$ to obtain the best-fit present values of $\Omega_{m0}$, $\Omega_{r0}$, and $H_{0}$. Then, we use these best-fit values of energy parameters to investigate cosmological parameters such as the deceleration parameter, the effective equation of state $\omega_{eff}$, and the energy density parameters $\Omega_{m}$, $\Omega_{r}$, and $\Omega_{f}$ to learn more about the components and history of the expanding universe. We found an effective EoS parameter in the range $-1\le \omega_{eff}\le\frac{1}{3}$ with a deceleration-acceleration transition redshift value of $z_{t}=0.6377, 0.6424$ along two datasets cosmic chronometer (CC) and Pantheon SNIa, respectively., Comment: 21 pages, 6 figures, Revision submitted to IJGMMP Journal

In this paper, we investigate some exact cosmological models in Myrzakulov $F(T,Q)$ gravity or the Myrzakulov gravity-III (MG-III) proposed in [arXiv:1205.5266], with observational constraints. The MG-III gravity is some kind of unification of two known gravity theories, namely, the $F(T)$ gravity and the $F(Q)$ gravity. The field equations of the MG-III theory are obtained by regarding the metric tensor and the general affine connection as independent variables. We then focus on the particular case in which the $F(T,Q)$ function characterizing the aforementioned metric-affine models is linear that is $F(T,Q)=\lambda T+\mu Q$. We investigate this linear case and consider a Friedmann-Lema\^{i}tre-Robertson-Walker background to study cosmological aspects and applications. We have obtained three exact solutions of the modified field equations in different cases $T$ and $Q$, in the form of Hubble function $H(t)$ and scale factor $a(t)$ and placed observational constraints on it through the Hubble $H(z)$ datasets on it using the MCMC analysis. We have investigated the deceleration parameter $q(z)$, effective EoS parameters and a comparative study of all three models with $\Lambda$CDM model has been carried out., Comment: 33 pages, 11 figures. arXiv admin note: text overlap with arXiv:2403.11604

We investigate some FLRW cosmological models in the context of Metric-Affine $F(R,Q)$ gravity, as proposed in [arXiv:1205.52666]. Here, $R$ and $Q$ are the curvature and nonmetricity scalars using non-special connections, respectively. We get the modified field equations using a flat Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) metric. We then find a connection between the Hubble constant $H_{0}$, the density parameter $\Omega_{m0}$, and the other model parameters in two different situations involving scalars $u$ and $w$. Next, we used new observational datasets, such as the cosmic chronometer (CC) Hubble datasets and the Pantheon SNe Ia datasets, to determine the optimal model parameter values through MCMC analysis. Using these best-fit values of model parameters, we have discussed the results and behavior of the derived models. We have also discussed the AIC and BIC criteria for the derived models in the context of $\Lambda$CDM. We have found that the geometrical sector dark equation of state parameter $\omega_{de}$ behaves just like a dark energy candidate. We have found that both models are transit phase models and Model-I approaches to the Lambda CDM model in the late-time universe and Model-II approaches to quintessence scenarios., Comment: 22 pages, 10 figures

In this paper, we have investigated some exact cosmological models in Myrzakulov gravity using a flat Friedmann-Lematre-Robertson-Walker (FLRW) spacetime metric. We have considered the modified Lagrangian function as $F(R,T)=R+\lambda T$, where $R, T$ are respectively the Ricci curvature scalar and the torsion scalar with respect to non-special connection, and $\lambda$ is a model parameter. We have obtained two exact solutions in two different situations for the scale factor $a(t)$. Using this scale factor, we have obtained various geometrical parameters to investigate cosmological properties of the universe. We have obtained the best fit values of model parameters through the MCMC analysis of two types latest observational datasets like $H(z)$ and Pantheon SNe Ia samples, with $1-\sigma, 2-\sigma$ \& $3-\sigma$ regions. We have performed a comparative and relativistic study of geometrical and cosmological parameters. In model-I, we have found that the effective equation of state (EoS) parameter $\omega_{eff}$ varies in the range $-1\le\omega_{eff}\le0$ while in the model-II, it varies as $-1.031\le\omega_{eff}\le0$. We have found that both models are transit phase (decelerating to accelerating) universe with transition redshift in the range $0.6

In the present paper, we investigate some exact cosmological models in Myrzakulov $F(R,T)$ gravity theory. We have considered the arbitrary function $F(R, T)=R+\lambda T$ where $\lambda$ is an arbitrary constant, $R, T$ are respectively, the Ricci-scalar curvature and the torsion. We have solved the field equations in a flat FLRW spacetime manifold for Hubble parameter and using the MCMC analysis, we have estimated the best fit values of model parameters with $1-\sigma, 2-\sigma, 3-\sigma$ regions, for two observational datasets like $H(z)$ and Pantheon SNe Ia datasets. Using these best fit values of model parameters, we have done the result analysis and discussion of the model. We have found a transit phase decelerating-accelerating universe model with transition redshifts $z_{t}=0.4438_{-0.790}^{+0.1008}, 0.3651_{-0.0904}^{+0.1644}$. The effective dark energy equation of state varies as $-1\le\omega_{de}\le-0.5176$ and the present age of the universe is found as $t_{0}=13.8486_{-0.0640}^{+0.1005}, 12.0135_{-0.2743}^{+0.6206}$ Gyrs, respectively for two datasets., Comment: 22 pages, 11 figures

In this paper, we have investigated an anisotropic cosmological model in $f(Q)$ gravity with string fluid in LRS Bianchi type-I universe. We have considered the arbitrary function $f(Q)=Q+\alpha\sqrt{~Q}+2\Lambda$ where $\alpha$ is model free parameter and $\Lambda$ is the cosmological constant. We have established a relationship between matter energy density parameter $\Omega_{m}$ and dark energy density parameter $\Omega_{\Lambda}$ through Hubble function using using constant equation of state parameter $\omega$. We have made observational constraint on the model using $\chi^2$-test with observed Hubble datasets $H(z)$ and SNe Ia datasets, and obtained the best fit values of cosmological parameters. We have used these best fit values in the result and discussion. We have discussed our result with cosmographic coefficients and found a transit phase dark energy model. Also, we analyzed the Om diagnostic function for anisotropic universe and found that our model is quintessence dark energy model., Comment: 24 pages, 12 Figures

The present research paper is an investigation of dark energy nature of logarithmic $f(R, T)$-gravity cosmology in a flat FLRW space-time universe. We have derived modified Einstein's field equations for the function $f(R, T)=R-16\pi G\alpha\ln(T)$ where $R$ is the Ricci scalar curvature, $T$ is the trace of the stress energy momentum tensor and $\alpha$ is a model parameter. We have solved field equations in the form of two fluid scenario as perfect-fluid and dark-fluid, where dark fluid term is derived in the form of perfect fluid source. We have made an observational constraints on the cosmological parameters $\Omega_{(m)}, \omega^{(de)}$ and $H_{0}$ using $\chi^{2}$ test with observational datasets like Pantheon sample of SNe Ia and $H(z)$. With these constraints we have discussed our model with deceleration parameter $q$, energy parameters $\Omega_{(m)}, \Omega_{(de)}$, EoS parameter $\omega^{(de)}$ etc. Also, we have done Om diagnostic analysis. The derived $f(R, T)$ model shows a quintessence dark energy model $\omega^{(de)}>-1$ and late-time universe approaches to $\Lambda$CDM model., Comment: 16 pages, 8 figures

In this article, we have discussed the results of our investigation. We consider an anisotropic viscous cosmological model of (LRS) Bianchi type I spacetime universe filled with a viscous fluid under $f(Q)$ gravity. We have studied the modified $f(Q)$ gravity with quadratic form $f(Q)=\alpha Q^{2}+\beta$, where $Q$ is called as a non-metricity scalar and $\alpha $, $\beta$ are positive constants. We obtain the modified Einstein field equation by considering the viscosity coefficient $\xi(t)=\xi_{0}H$ and obtained the scale factor $a(t)=2~sinh\left (\frac{m+ 2} {6}\sqrt{\frac{\xi_{0}}{\alpha(2m+1)}}t\right)$.We applied the observational constraint on the apparent magnitude $m(z)$ using the $\chi^{2}$ test formula with observational data set like JLA or Union 2.1 compilation and obtained the best approximate values of the model parameters ${ m,\alpha, H_{0} \xi_{0}}$. We have analyzed our model and found a transit phase quintessence anisotropic accelerating universe. We also examined the bulk viscosity equation of state (EoS) parameter $\omega_{v}$ and obtained its current value as $\omega_{v}<-1/3$, which shows the dark energy dominant model, cosmological constant, phantom, and super-phantom dark energy models, and tends to the $\Lambda$CDM value ($\omega_{v}=-1$) in the late time. We also estimate the current age of the universe as $t_{0}\approx13.6$ Grys and analyze the Statefinder parameters with $(s,r)\to(0,1)$ as $t \to \infty$., Comment: 19 pages, 14 figures

This research paper deals with a transit dark energy cosmological model in $f(R, L_{m})$-gravity with observational constraints. For this, we consider a flat FLRW space-time and have taken a cosmological cosntant-like parameter $\beta$ in our field equations. The model has two energy parameters~ $\Omega_{m0}~ and~ \Omega_{\beta0}$, which govern the mechanism of the universe, in particular its present accelerated phase. To make the model cope with the present observational scenario, we consider three types of observational data set: $46$ Hubble parameter data set, SNe Ia $715$ data sets of distance modulus and apparent magnitude, and $40$ datasets of SNe Ia Bined compilation in the redshift $0\leq z<1.7$. We have approximated the present values of the energy parameters by applying $R^{2}$ and $\chi^{2}$-test in the observational and theoretical values of Hubble, distance modulus, and apparent magnitude parameters. Also, we have measured the approximate present values of cosmographic coefficients $\{H_{0}, q_{0}, j_{0}, s_{0}, l_{0}, m_{0}\}$. It is found that our approximated value-based model fits best with the observational module. We have found that as $t\to\infty$ (or $z\to 0$) then $\{q, j, s, l, m\}\to\{-1, 1, 1, 1, 1\}$. The cosmic age of the present universe is also approximated and comes up to the expectation. Our model shows a transit phase of the present accelerating universe with a deceleration in the past and has a transition point., Comment: 22 pages, 17 figures

The present study deals with a flat FRW cosmological model filled with perfect fluid coupled with the zero-mass scalar field in the higher derivative theory of gravity. We have obtained two types of universe models, the first one is the accelerating universe (power-law cosmology) and the second one is the transit phase model (hyperbolic expansion-law). We have obtained various physical and kinematic parameters and discussed them with observationally constrained values of $H_{0}$. The transit redshift value is obtained $z_{t}=0.414$ where the transit model shows signature-flipping and is consistent with recent observations. In our models, the present values of EoS parameter $\omega_{0}$ crosses the cosmological constant value $\omega_{0}=-1$. Also, the present age of the universe is calculated., Comment: 12 pages, 21 figures

In this paper, we have developed a new cosmological model in Einstein's modified gravity theory using two types of modification.(i) Geometrical modification, in which we have used Lyra's geometry in the left hand side of the Einstein field equations (EFE) and (ii) Modification in gravity (energy momentum tensor) on right hand side of EFE, as per Brans-Dicke (BD) model. With these two modifications, we have investigated a spatially homogeneous and anisotropic Bianchi type-I cosmological models of Einstein's Brans-Dicke theory of gravitation in Lyra geometry. The model represents accelerating universe at present and decelerating in past and is considered to be dominated by dark energy. Gauge function $\beta$ and BD-scalar field $\phi$ are considered as a candidate for the dark energy and is responsible for the present acceleration. The derived model agrees at par with the recent supernovae (SN Ia) observations. We have set BD-coupling constant $\omega$ to be greater than 40000, seeing the solar system tests and evidences. We have discussed the various physical and geometrical properties of the models and have compared them with the corresponding relativistic models., Comment: 20 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1406.7636, arXiv:1710.09269, arXiv:1710.07281, arXiv:1203.0917 by other authors