Narrow Results

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.

In this paper, we have presented a model of the Friedmann–Lemaitre–Robertson–Walker (FLRW) universe filled with matter and dark energy (DE) fluids by assuming an ansatz that deceleration parameter (DP) is a linear function of the Hubble constant. This results in a time-dependent DP having decelerating–accelerating transition phase of the universe. This is a quintessence model ${\omega }_{(de)}\ge -1$. The quintessence phase remains for the period $(0\le z\le 0.5806)$. The model is shown to satisfy current observational constraints. Various cosmological parameters relating to the history of the universe have been investigated.

In this paper, a class of $f(R)$ gravitational models with coupling between matter and geometry have been studied by a dynamical approach in cosmology. The result shows that both the cosmic radiation dominated era and the late-time cosmic accelerated expansion can be achieved in this class of models. Moreover, the corresponding parameters are constrained as well.

Within the framework of quantum gravity and modified entropy-area formalism, the Tsallis holographic dark energy is an effort to peep into a mysterious content of the Universe, the dark energy, to analyze its nature. The Tsallis parameter $\delta$ provides the main characteristic of the Tsallis holographic dark energy. Opting the value of Tsallis parameter $\delta \le 2$, a quintessence scalar field description of the Tsallis holographic dark energy model can be obtained. In this work, we present this quintessential explanation of the Tsallis holographic dark energy with $\delta \le 2$ and reconstruct the dynamics of the scalar field and the potential of quintessence.

This work analyzes a power law solution under $f(R,T)$ gravity for an isotropic and homogeneous universe. To construct $f(R,T)$ gravity model, we consider the functional form of $f(R,T)$ as the sum of two independent functions of the Ricci scalar R and the trace of the energy–momentum tensor T, i.e. $f(R,T)=R+\xi RT$, with $\xi$ being a positive constant where we study the cosmological model under the following two cases: (i) $f_1(R)=f_2(R)=R$ and (ii) $f_3(T)=\xi T$. In the framework of $f(R,T)$ gravity with homogeneous and isotropic spacetime, the constructed model yields several features on application of the scale factor $a=\alpha t^{\beta }$. We employed the Markov Chain Monte Carlo (MCMC) approach to get model parameters $\alpha$, $\beta$ and $H_0$ over a redshift range of $0\le z\le 1.965$. The model parameter’s restricted values are listed below: $H_0=67.098_{-1.792}^{+2.148}$ km ${\text{s}}^{-1}$Mpc${}^{-1}$, $H_0=67.588_{-2.170}^{+2.229}$km${\text{s}}^{-1}$ Mpc${}^{-1}$, $H_0=66.270_{-2.181}^{+2.215}$kms${}^{-1}$ Mpc${}^{-1}$, $H_0=65.960_{-1.834}^{+2.380}$kms${}^{-1}$Mpc${}^{-1}$, $H_0=66.274_{-1.864}^{+2.015}$kms${}^{-1}$Mpc${}^{-1}$. The model was constrained using the Hubble parameter ($H(z)$) dataset, Baryon Acoustic Oscillations (BAO) dataset, Pantheon dataset, joint $H(z)$ + Pantheon dataset and collective $H(z)$ + BAO + Pantheon dataset. The results from the Planck collaboration group are consistent with these calculated Ho observed values. In order to study and analyze the model, we first look at how the energy circumstances affected our power law assumption. The validity of the model has also been evaluated using the $Om$ diagnostic and the jerk parameter, which are state finding diagnostic tools. We find that the model under investigation agrees with the observed fingerprints within a certain range of constraints.

We have analyzed the Barrow holographic dark energy (BHDE) in the framework of flat FLRW universe by considering the various estimations of Barrow exponent △. Here, we define BHDE, by applying the usual holographic principle at a cosmological system, for utilizing the Barrow entropy rather than the standard Bekenstein–Hawking. To understand the recent accelerated expansion of the universe, consider the Hubble horizon as the IR cutoff. The cosmological parameters, especially the density parameter $({\mathrm{\Omega }}_D)$, the equation of the state parameter $({\omega }_D)$, energy density $({\rho }_D)$ and the deceleration parameter $(q)$ are studied in this paper and found the satisfactory behaviors. Moreover we additionally focus on the two geometric diagnostics, the statefinder $(r,s)$ and $O_m(z)$ to discriminant BHDE model from the $\mathrm{\Lambda }$CDM model. Here we determined and plotted the trajectories of evolution for statefinder $(r,s)$, $(r,q)$ and $O_m(z)$ diagnostic plane to understand the geometrical behavior of the BHDE model by utilizing Planck 2018 observational information. Finally, we have explored the new Barrow exponent △, which strongly affects the dark energy equation of state that can lead it to lie in the quintessence regime, phantom regime and exhibits the phantom-divide line during the cosmological evolution.

In this paper, we have investigated the physical behavior of cosmological models in the framework of modified teleparallel gravity. This model is established using a Rényi holographic dark energy (RHDE) model with a Hubble cut-off. Here, we have considered a homogeneous and isotropic Friedman universe filled with perfect fluid. The physical parameters are derived for the present model in compliances with 43 observational Hubble data sets. The equation-of-state parameter in terms of $H(z)$ describes the transition of the universe between phantom and nonphantom phases in the context of $f(T)$ gravity. Our model shows the violation of strong energy condition and the weak energy condition over the accelerated phantom regime. We also observed that these models occupy freezing regions through ${\omega }_D$–${\omega }_D^{\prime }$ plane. Consequently, our RHDE model is supported to the consequences of general relativity in the framework of $f(T)$ modified gravity.

We propose a large class of nonsingular cosmologies of arbitrary spatial curvature whose cosmic history is determined by a primeval dynamical Λ(t)-term. For all values of the curvature, the models evolve between two extreme de Sitter phases driven by the relic time-varying vacuum energy density. The transition from inflation to the radiation phase is universal and points to a natural solution of the graceful exit problem regardless of the values of the curvature parameter. The flat case recovers the scenario recently discussed in the literature [Perico et al., Phys. Rev. D88 (2013) 063531]. The early de Sitter phase is characterized by an arbitrary energy scale H_I associated to the primeval vacuum energy density. If H_I is fixed to be nearly the Planck scale, the ratio between the relic and the present observed vacuum energy density is ρ_vI/ρ_v0 ≃ 10¹¹⁸.

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–Lemaitre–Robertson–Walker (FLRW) Universe within the framework of the f (Q,T) modified gravity theory (where Q is the nonmetricity and T is the trace of the energy–momentum tensor) recently proposed by Y. Xu et al. [Eur. Phys. J. C 79 (2019) 708], which is an extension of f (Q) gravity with the addition of the T term. Here, we presume a specific form of $f(Q,T)=\alpha Q+\beta Q^2+\gamma T$ where $\alpha$, $\beta$ and $\gamma$ are free model parameters, and obtained the exact solutions by assuming the cosmic time-redshift relation as $t(z)=\frac{n{t}_0}{m}g(z)$ which produces the Hubble parameter of the form $H(z)=\frac{m{H}_0}{m+n}[\frac{1}{g(z)}+1]$, where m and n are the nonnegative constants, we find the best values for them using 57 data points of the Hubble parameter H(z). Also, we find the behavior of different cosmological parameters as the deceleration parameter (q), energy density $(\rho )$, pressure (p) and equation of state (EoS) parameter $(\omega )$ 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 found that our model behaves similarly to the quintessence Universe.

In this work, we explore the Tsallis holographic dark energy (THDE) model with IR cutoff as Granda–Oliveros horizon describing the Universe experiencing an accelerating expansion phase in the framework of flat Friedmann–Lemaître–Robertson–Walker (FLRW) Universe. The Universe evolution from earlier decelerated to the current accelerated phase is exhibited by the deceleration parameter acquired in the THDE model. By the value of the Tsallis parameter $\delta$, the equation of state (EoS) parameter for the THDE model represents the rich behavior of the Cosmos as, the quintessence era (${\omega }_T\ge -1$), crossing the phantom divide line and phantom era (${\omega }_T<-1$). The squared sound speed $v_s^2$ also suggests that the THDE model is classically stable at present. Also, the correspondence with the quintessence and phantom scalar field for the THDE model is analyzed to describe the accelerated expansion of the Universe.

In this work, we propose a non-interacting model of Barrow holographic dark energy (BHDE) using Barrow entropy in a spatially flat FLRW Universe considering the IR cutoff as the Hubble horizon. We study the evolutionary history of important cosmological parameters, in particular, deceleration parameter, equation of state (EoS) parameter, the BHDE and matter density parameter, and also observe satisfactory behaviors in the BHDE model. The stability of the BHDE model has been examined by squared sound speed $v_s^2$. In addition, to describe the accelerated expansion of the Universe, the correspondence of the BHDE model with the quintessence scalar field has been reconstructed.

$f(Q,T)$ 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 have investigated the physical behavior of cosmological models in modified Teleparallel gravity with a general function $f(T)=\alpha T+\beta {(-T)}^n$ where $\alpha ,\beta$ and $n$ are model parameters and $T$ is the torsion scalar. We have considered a homogeneous and isotropic Friedman universe filled with perfect fluid. We have derived the deceleration parameter $q(\omega ,H(z))$ in terms of equation of state (EoS) parameter $\omega$ and Hubble parameter $H(z)$. We have investigated the variation of $q$ over the observed values of Hubble constant in various observations within the range of redshift $0.07\le z\le 2.30$. Also, we have studied effective energy density ${\rho }^{\mathrm{\text{eff}}}$, effective pressure $p^{\mathrm{\text{eff}}}$ and effective EoS parameter ${\omega }^{\mathrm{\text{eff}}}$. We have observed that the second term of $f(T)$ function behaves just like variable cosmological term $\mathrm{\Lambda }$ (${\omega }^{\mathrm{\text{eff}}}\approx -1$) at late-time universe and causes the acceleration in expansion and works just like dark energy candidates. Also, we have evaluated the age of the present universe for various stages of matter $p=\omega \rho$ and various $f(T)$ functions.

In the present work, we consider the recently proposed non-interacting Barrow holographic dark energy (Int. J. Geom. Methods Mod. Phys.18(01) (2021) 2150014, doi:10.1142/S0219887821500146) with Hubble horizon as IR cutoff in a flat FLRW universe. We examine the evolutionary behavior of deceleration parameter and equation of state parameter for the different Barrow exponent $\mathrm{\Delta }$, and observe suitable behavior in the model. We choose $\mathrm{\Delta }>2$ in the non-interacting Barrow holographic dark energy which is explained by a phantom scalar field, then we exhibit the phantomic narration of the Barrow holographic dark energy with $\mathrm{\Delta }>2$ and reconstruct the potential of the phantom scalar field.

In this paper, we have investigated the physical behavior of cosmological models in modified teleparallel gravity with a linear function $f(T)=\alpha T+\beta$ where $\alpha$ and $\beta$ are model parameters and $T$ is the torsion scalar. We have considered a homogeneous and isotropic Friedman universe filled with bulk viscosity fluid. We have solved the field equations for the scale factor $a(\tau )$ and found $a(\tau )=c_1{[\mathrm{\text{sinh}}(n_2\tau )]}^{n_3}$ where $n_2=\sqrt{\frac{\beta (1+\omega )[{\kappa }^2{\xi }_0-3(1+\omega )(1+\alpha )]}{8}}$ and $n_3=\frac{2}{[{\kappa }^2{\xi }_0-3(1+\omega )(1+\alpha )]}$ and $c_1$ is an integrating constant, $\omega$ is the equation of state (EoS) for normal matter and ${\xi }_0$ is generated from bulk viscosity fluid. We have calculated the several cosmological parameters for this scale factor and studied their physical and geometrical behavior along with the observational data sets $H(z)$ and Union $2.1$ compilation of SNe Ia data sets. We have observed that the $\beta$ factor reveals the presence of cosmological constant and for $\beta =0$, the acceleration drives by the bulk viscosity of the fluid and it behaves just like dark energy model without cosmological constant. We have studied the effective EoS ${\omega }_{\mathrm{\text{eff}}}$ and found $-0.2807\le {\omega }_{\mathrm{\text{eff}}}\le -0.1760$. We have evaluated the age of the present universe as $13.87$ Gyrs. Also, we have studied the nature of deceleration parameter with the signature-flipping point at $z_t=0.5,1.14$ and the present value of deceleration parameter $q_0$ is obtained as $-0.3303,-0.4152$, respectively, for both observational datasets.

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 $f(Q)$ 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 $f(Q)$ as $f(Q)=\alpha Q^{n+1}+\beta ,$ (where $\alpha$, $\beta$, and $n$ are free model parameters) that contains two models: Linear ($n=0$) and nonlinear ($n\ne 0$). 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).

At present, we are aware that some recent changes in the cosmos cannot be explained by the standard interpretation of general relativity. In order to do so, we used the reconstruction scheme for recently proposed $f(T)$ gravity to look into the universe’s accelerated expansion. Here, we define the transit scale factor (TSF), a scale factor used to explain several geometrical and physical aspects. Then, using the Markov Chain Monte Carlo (MCMC) method, we estimate the best fit values for the model parameters imposed from data from Hubble’s, Standard candles and Uncorrelated BAO. The cosmos is moving from the deceleration phase into the acceleration phase, according to the evolution of the deceleration parameter. Also, we review the statefinder’s diagnostic elements $(r,s)$. We came to the conclusion that the reconstructed $f(T)$ models indicate that the universe is in an accelerating phase at $z=0$ and acts like quintessence models, and that it approaches $\mathrm{\Lambda }$CDM models at $z=-1$ which seem to be in good accord with the observations.

In this paper, we investigate the dynamical behavior of the universe with a flat FLRW model in $f(R,G)$ gravity, where $R$ and $G$ both signify the Ricci scalar and Gauss–Bonnet invariant. Furthermore, in order to determine the model’s behavior, it must have the late-time universe’s behavior, which involves both an accelerated expansion as well as ending in a big rip. We present a model that begins with a point-type singularity, i.e. a point with zero volume and infinite energy density, by using parametrization of the scale factor $a(t)$. The model’s actions are accelerating and expanding at the moment, and $\mathrm{\Lambda }$CDM in late times. Our extensive analysis encompasses the energy conditions, dynamics of certain model solutions and additional cosmological tests through a dominant model. Finally, the proposed framework acts exactly like a quintessence dark energy model in the current time and is reliable with standard cosmology $\mathrm{\Lambda }$CDM in late times.

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 ($-1.65\le {\omega }^{\mathrm{\text{eff}}}\le -0.79$).