Narrow Results

In this paper, we investigate the constrained transit cosmological models in the most recently proposed modified gravity theory, $f(R,L_m,T)$-gravity. We obtain the modified field equations for a flat homogeneous and isotropic Friedmann–Lemaître–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 ${\mathrm{\Omega }}_{m0}$, ${\mathrm{\Omega }}_{r0}$, and ${\mathrm{\Omega }}_{f0}$ and the Hubble function. After that, we made observational constraints on $H(z)$ to obtain the best-fit present values of ${\mathrm{\Omega }}_{m0}$, ${\mathrm{\Omega }}_{r0}$, 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 ${\omega }_{\mathrm{\text{eff}}}$, and the energy density parameters ${\mathrm{\Omega }}_m$, ${\mathrm{\Omega }}_r$, and ${\mathrm{\Omega }}_f$ to learn more about the components and history of the expanding universe. We found an effective EoS parameter in the range $-1\le {\omega }_{\mathrm{\text{eff}}}\le \frac{1}{3}$ with a deceleration–acceleration transition redshift value of $z_t=0.6377,0.6424$ along two datasets cosmic chronometer (CC) and Pantheon SNIa, respectively.

In this paper, we investigate dust-fluid flat cosmological models in the recently proposed modified $f(R,T,L_m)$-gravity theory. We derive the field equations for the flat FLRW spacetime metric for the arbitrary function $f(R,T,L_m)=\frac{R}{2}+\alpha T+\beta L_m^n-\gamma$, where $R$ is the Ricci curvature scalar, $L_m$ is the matter Lagrangian, $T$ is the trace of the energy–momentum tensor $T_{ij}$, and $\alpha$, $\beta$, $\gamma$, and $n$ are the model parameters. We solve these equations to obtain the Hubble function in terms of matter energy density parameters ${\mathrm{\Omega }}_{\alpha 0}$, ${\mathrm{\Omega }}_{\beta 0}$, ${\mathrm{\Omega }}_{\gamma 0}$, and Hubble constant $H_0$. Then, we use the cosmic chronometer (CC) Hubble points dataset and the Pantheon dataset to do MCMC analysis of the Hubble function and find the best fit model parameters for the lowest ${\chi }^2$ values. Subsequently, we investigate the effective equation of state parameter ${\omega }_{\mathrm{\text{eff}}}$ and deceleration parameter $q(z)$ for the present past epoch of the universe. We also perform analysis for energy conditions and statefinder parameters to discuss the different stages of the dark energy models.

This work explores the dark energy nature of logarithmic $f(R,L_m)$-gravity models with observational constraints, where $L_m$ represents the matter Lagrangian for perfect fluid and R is the Ricci-scalar curvature. With a matter Lagrangian $L_m=\rho$, a flat FLRW space–time metric and an arbitrary function $f(R,L_m)=\frac{R}{2}+L_m-\mu ln{L}_m$, where $\mu$ is a positive model parameter, we have derived the field equations of this model. By using the Hubble function, we have been able to solve the energy conservation equation and create a relationship between ${\mathrm{\Omega }}_{m0}$, ${\mathrm{\Omega }}_{q0}$ and ${\mathrm{\Omega }}_{\mu 0}$. Using the most recent two observational datasets as 32 $H(z)$ and 1048 Pantheon SNe Ia datasets, we conducted MCMC analysis. We have obtained best fit values of model parameters with $1-\sigma ,2-\sigma ,3-\sigma$ errors and using these values, we have explored the cosmological properties of the model. We have performed om diagnostic analysis for the model and estimated the present age of the universe. Thus our derived model presents a transit phase decelerating to accelerating model without dark energy term $\mathrm{\Lambda }$. We found that the effective equation of state parameter is in the range $-1\le \omega \le 0$ over $-1\le z<\infty$ with present value $\omega \approx -0.6971,-0.7120$.

This paper is an attempt to revisit the Friedmann–Robertson–Walker (FRW) cosmological models under the new scenario of observational cosmology, which has established that the current universe is expanding with an increasing rate, in contrast to the earlier belief that the rate of expansion is constant or slowing down. This paper represents a model which encompasses both, earlier decelerating and the current accelerating universe, passing through a transition phase. The universe is assumed to be filled with two fluids, barotropic and dark energy. We have considered two cases; first, when these fluids are assumed to be non-interacting and second, when they interact with each other. Some physical, kinematic and geometric properties of the model are also discussed along with the acceptability and stability of the solution. The results found are very compatible with the established results as well as recent observations.

In this paper, in the framework of the Brans–Dicke [Phys. Rev. 124 (1961) 925] Gravitation theory, we propose to study the spatially homogeneous, anisotropic and axially symmetric model filled with dark matter and dark energy. Here, we consider the modified holographic Ricci dark energy proposed by Chen and Jing [Phys. Rev. B 679 (2009) 144] as a feasible state of darkness. To achieve a solution, we consider the time-dependent deceleration parameter, which contributes to the average scale factor of $a(t)=\mathrm{\text{exp}}\left(\right.\frac{1}{\beta }\sqrt{2\beta t+\alpha }\left)\right.$, where $\alpha >0$ and $\beta >0$ are arbitrary constants. We have derived field equations of Brans–Dicke theory of gravitation with the help of an axially symmetric anisotropic Bianchi-type space-time. We have determined the cosmological parameters, namely, deceleration parameter, matter energy density, anisotropic dark energy density, BD scalar field, skewness parameter, EoS parameter and jerk parameter. Here, the various phenomena like the Big Bang, expanding the universe, and shift from anisotropy to isotropy are observed in the model. A comprehensive physical debate of these dynamic parameters is provided through a graphical representation. We observe that we have a quintessence model that exhibits a smooth transition from decelerated stage to an accelerated phase of the universe. This situation is in complete agreement with the modern cosmology scenario. Some physical and geometric behaviors are also discussed and discovered to be in excellent agreement with SNe Ia Supernova’s latest observations.

In this paper, we have discussed string cosmological model within the framework of $f(R,T)$ theory of gravity in homogeneous but anisotropic Bianchi Type-II space-time. We have considered cosmic string as a source of energy–momentum tensor. We get the solution of the corresponding field equations by assuming deceleration parameter $q(t)=-1+\frac{\beta }{\sqrt{2\beta t+k}}$, which is time-dependent (here, $k$ and $\beta$ are arbitrary constants). This particular form of scale factor enables us to explain the two scenarios, (i) By using recent constraints ($H_0=73.8$, $q_0=-0.73$) from supernovae type Ia union data (Cunha, Kinematic constraints to the transition redshift from supernovae type Ia union data, Phys. Rev. D79 (2009) 047301), we find the values of arbitrary constants $\beta$ and $k$ for which we have derived a cosmological model showing accelerating expansion universe ($q<0$) only throughout the evolution and (ii) By using the recent constraints ($H_0=73.8$, and $q_0=-0.54$) from SNIa data in combination with BAO and CMB observations (Giostri et al. From cosmic deceleration to acceleration: new constraints from SN Ia and BAO/CMB, J. Cosmol. Astrophys.3 (2012) 27), we find the values of arbitrary constants for which we have derived a cosmological model with phase transition from early decelerating ($q>0$) to the present accelerating ($q<0$) universe. Also, for the model, we have evaluated and discussed the various physical and kinematic parameters. We have also shown the variation of these cosmological parameters graphically for specific values of the constants. The stability and physical viability are also discussed for the derived models using some recently developed diagnostic tools.

$f(Q,T)$ gravity is a recently proposed modified theory of gravity due to Xu et al. ($2019$). It is an extension of the symmetric teleparallel gravity, in which the gravitational action is given by an arbitrary function $f(Q,T)$ of the non-metricity tensor $Q$ and the trace of energy-momentum tensor $T$. In this paper also, we have investigated the cosmological model with Friedmann–Lemaitre–Robertson–walker (FLRW) Universe in $f(Q,T)$ theory with $f(Q,T)=\alpha Q^n+\beta T$. Applying the energy conservation condition $\dot{\rho }+3H(\rho +p)=0$, we have obtained the various cosmological parameters viz. Hubble parameter $H(z)$, deceleration parameter $q(z)$, etc. in terms of redshift $z$. Using the available observational Hubble datasets $H(z)$, the best fit values of the model parameters are determined by the $R^2$-test formula. For these obtained values of model parameters, our model represents a transit cosmological model with past decelerating to present accelerating expansion phase of the Universe with the present value $q_0=-0.63$. The point of signature-flipping (transition) is calculated as $z_t=0.469$. We have analyzed the variations of physical parameters viz. matter energy density $\rho$, isotropic pressure $p$, equation of state $\omega =\frac{p}{\rho }$ with respect to redshift $z$ and coupling parameter $\beta$. For checking the viability of our derived model, we have tested energy conditions and also performed statefinder diagnosis. The age of the Universe is also calculated.

Xu et al. (Eur. Phys. J. C79 (2019) 708) have anticipated the theory of Gravity. The modified study of $f(Q,T)$ is elucidated here as Cosmological model. In it the action holds a role as a capricious arbitrary function $f(Q,T)$. At this juncture $Q$ functions as non-metricity and for matter fluid, $T$ outlines as energy-momentum tensor. The function $f(Q,T)$ quadratic in $Q$ and linear in $T$ as $f(Q,T)=\alpha Q+\beta Q^2+\gamma T$ has been taken as our research in which $\alpha$, $\beta$ and $\gamma$ stand as model parameters, induced by $f(R,T)$ gravity. A range of cosmological parameters have been attained by us such as in Universe viz. Hubble parameter $H$, Friedmann–Lemaitre–Robertson–Walker (FLRW), deceleration parameter $q$, etc. in terms of scale-factor and in terms of redshift $z$ by confining to the law of energy-conservation. The fittest values of the model parameters have been acquired by us as the observational constrictions on the model, by utilizing the accessible data sets like Hubble data sets $H(z)$, union $2.1$ compilation of SNe Ia data sets and Joint Light Curve Analysis (JLA) data sets. We have applied $R^2$-test formula. The values of various observational parameters have been premeditated by us viz. $H_0$, $q_0$, $t_0$ and state finder parameters $(s,r)$. They are absolutely very close to the standard cosmological models. It has also been observed by us that the deceleration parameter $q(z)$ exhibits signature-flipping (transition) point within the range $0.423\le z_t\le 0.668$. It is observed that it changes its phase from decelerated to accelerated expanding universe with equation of state (EoS) $-1.071\le \omega -0.96$ for $0\le z\le 3$.

In this paper, we study the mechanism of the cosmic model in the presence of generalized ghost pilgrim dark energy (GGPDE) and matter in locally rotationally symmetric (LRS) Bianchi type-I space-time by the utilization of new holographic DE in Saez–Ballester theory. Here, we discuss all the data for three scenarios, the first is supernovae type-Ia union data, the second is SN Ia data in combination with baryon acoustic oscillation and cosmic microwave background observations and the third is a combination with observational Hubble data and joint light-curve analysis observations. From this, we get a model of our universe, where transit state exists from deceleration to acceleration phase. Here, we have observed that the results yielded by cosmological parameters like ${\rho }_{\mathrm{\Lambda }}$ (energy density), equation of state ${\omega }_{\mathrm{\Lambda }}$, squared speed of sound $(v_s^2)$ and $({\omega }_{\mathrm{\Lambda }}$–${\omega }_{\mathrm{\Lambda }}^{\prime })$ are compatible with the recent observations. The $({\omega }_{\mathrm{\Lambda }}$–${\omega }_{\mathrm{\Lambda }}^{\prime })$ trajectories lie in both thawing and freezing regions and the correspondence of the quintessence field with GGPDE is also discussed. Some physical aspects of the GGPDE models are mainly highlighted.

In this paper, we investigated the general behaviors of the Tsallic holographic dark energy (THDE) model in general relativity. Here, we take the Bianchi $V{I}_0$ metric, which is homogeneous and anisotropic. We investigate the THDE models with the Hubble horizon and Granda–Oliveros (GO) cutoffs. We have studied the behavior of a few quantities, such as dark energy density $({\rho }_D,)$, matter-energy density $({\rho }_m)$, and skewness parameter $(\gamma )$ and discuss their physical significances. In our THDE models, the EoS parameter explains the universe’s evolution based on the value of the non-extensive or Tsallis parameter $\delta$. In addition, we develop the cosmographic parameters like, deceleration parameter $(q)$, jerk parameter $(j)$, lerk parameter $(l)$, snap parameter $(S)$ and maxout parameter $(m)$. We have explored the ${\omega }_D-{\omega }_D^{\prime }$ plane and the stability analysis of the THDE model by a perturbation method. We have also constructed a correspondence between the THDE model with quintessence. Some physical and geometrical behaviors of the models are also discussed.

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 $f(Q)=Q+\alpha \sqrt{Q}+2\mathrm{\Lambda }$, where $\alpha$ is model free parameter and $\mathrm{\Lambda }$ is the cosmological constant. We have established a relationship between matter energy density parameter ${\mathrm{\Omega }}_m$ and dark energy density parameter ${\mathrm{\Omega }}_{\mathrm{\Lambda }}$ through Hubble function 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.

In this paper, an attempt is made to construct a Friedmann–Lemaitre–Robertson–Walker model in $f(R,T)$ gravity with a perfect fluid that yields acceleration at late times. We take $f(R,T)$ as $R+8\pi \mu T$. As in the $\mathrm{\Lambda }$CDM model, we take the matter to consist of two components, viz., ${\mathrm{\Omega }}_m$ and ${\mathrm{\Omega }}_{\mu }$ such that ${\mathrm{\Omega }}_m+{\mathrm{\Omega }}_{\mu }=1$. The parameter ${\mathrm{\Omega }}_m$ is the matter density (baryons $+$ dark matter), and ${\mathrm{\Omega }}_{\mu }$ is the density associated with the Ricci scalar $R$ and the trace $T$ of the energy–momentum tensor, which we shall call dominant matter. We find that at present ${\mathrm{\Omega }}_{\mu }$ is dominant over ${\mathrm{\Omega }}_m$, and that the two are in the ratio 3:1–3:2 according to the three data sets: (i) 77 Hubble OHD data set, (ii) 580 SNIa supernova distance modulus data set and (iii) 66 pantheon SNIa data which include high red shift data in the range $0\le z\le 2.36$. We have also calculated the pressures and densities associated with the two matter densities, viz., $p_{\mu }$, ${\rho }_{\mu }$, $p_m$ and ${\rho }_m$, respectively. It is also found that at present, ${\rho }_{\mu }$ is greater than ${\rho }_m$. The negative dominant matter pressure $p_{\mu }$ creates acceleration in the universe. Our deceleration and snap parameters show a change from negative to positive, whereas the jerk parameter is always positive. This means that the universe is at present accelerating and in the past it was decelerating. State finder diagnostics indicate that our model is at present a dark energy quintessence model. The various other physical and geometric properties of the model are also discussed.

In this paper, we reconstruct an $f(T)$ function from $\mathrm{\Lambda }$CDM model and obtained field equations for this function $f(T)=\frac{T}{2}+c_1{(-T)}^{\frac{1}{2}}-2\mathrm{\Lambda }$ in a flat FLRW viscous-fluid dusty universe, where $T$ is the torsion scalar, $c_1$ is an arbitrary constant and $\mathrm{\Lambda }$ is the cosmological constant. We have solved the field equations and obtained an scale factor $a(t)=c_2\left[\right.\mathrm{\text{sinh}}\left(\right.\frac{2\mathrm{\Lambda }}{9{(1-{\xi }_0)}^2}t+\frac{c_1\mathrm{\Lambda }}{3(1-{\xi }_0)}\left)\right.{\left]\right.}^{\frac{3(1-{\xi }_0)}{2}},{\xi }_0\ne 1$ with $c_2$ as an integrating constant and ${\xi }_0$ is an arbitrary constant generated from viscous fluid, and this type of scale factor gives a time-dependent deceleration parameter. We have made observational constraints on Hubble parameter $H(z)$ and apparent magnitude $m(z)$ with observational datasets $H(z)$ data and SNe Ia data by applying ${\chi }^2$-test, to obtain the best-fit values of model parameters. Using these values of cosmological parameters, we have discussed our model results. We have obtained a transit phase accelerating quintessence dark energy model in viscous-fluid universe with effective equation of state ($-1.65\le {\omega }^{\mathrm{\text{eff}}}\le -0.79$).

In this investigation, we have observed an anisotropic Bianchi type-I dark energy universe model in $f(R,L_m)$ gravity with observational constraints, where $f(R,L_m)$ is an arbitrary function of Ricci-scalar curvature $R$ and matter Lagrangian $L_m$. For our investigation, we have considered a specific form of this function as $f(R,L_m)=\frac{R}{2}+\alpha L_m^n-\mathrm{\Lambda }$ with $\alpha ,n$ as model free parameters and $\mathrm{\Lambda }$ is the “cosmological constant”. We have solved the field equations analytically and established a relationship between energy parameters ${\mathrm{\Omega }}_m,{\mathrm{\Omega }}_k$ and ${\mathrm{\Omega }}_{\mathrm{\Lambda }}$ and obtained Hubble function $H(z)$ in terms of redshift $z$. We have compared this Hubble function with two observational datasets Union 2.1 plus bined and $H(z)$ for obtaining the best fit values of model parameters and energy parameters, by applying ${\chi }^2$-test. We have analyzed and discussed the results using these best fit values throughout the paper. We have found a accelerating transit phase phantom dark energy model which tends to $\mathrm{\Lambda }$CDM model at late-time universe.