Narrow Results

We investigate an isotropic and homogeneous flat dark energy model in $f(Q,C)$ gravity theory that is linear in non-metricity Q and quadratic in boundary term C as $f(Q,C)=Q+\alpha C^2$, where $\alpha$ is a model parameter. We have solved the field equations in flat Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetime geometry and considered a relation in the form of Hubble function in total energy density parameters ${\mathrm{\Omega }}_{m0}$, ${\mathrm{\Omega }}_{0(Q,C)}$, and Hubble constant $H_0$. We have compared our results with two observational datasets $H(z)$ and Pantheon SNe Ia datasets by using MCMC analysis and have obtained the best fit present values of parameters. We have used these best fit values throughout in result analysis and discussion. We have found the equation of state (EoS) parameter as $-1\le \omega \le 0.2$ over $-1\le z\le 3$. We have also investigated the Om diagnostic function and present age of the universe for these two datasets.

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 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 Friedman–Lamatre–Robertson–Walker (FLRW) space-time and have taken a cosmological constant-like parameter $\beta$ in our field equations. The model has two energy parameters ${\mathrm{\Omega }}_{m0}and{\mathrm{\Omega }}_{\beta 0}$, 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 $0\le z<1.7$. 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.

This 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 scenarios as perfect fluid and dark fluid, where dark fluid term is derived in the form of perfect fluid source. We have made an observational constraint on the cosmological parameters ${\mathrm{\Omega }}_{(m)},{\omega }^{\mathrm{\text{(de)}}}$ 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 ${\mathrm{\Omega }}_{(m)},{\mathrm{\Omega }}_{\mathrm{\text{(de)}}}$, EoS parameter ${\omega }^{\mathrm{\text{(de)}}}$, etc. Also, we have done Om diagnostic analysis. The derived $f(R,T)$ model shows a quintessence dark energy model ${\omega }^{\mathrm{\text{(de)}}}>-1$ and late-time universe approaches to $\mathrm{\Lambda }$ CDM model.

In the recently suggested modified non-metricity gravity theory with boundary term in a flat FLRW spacetime universe, dark energy scenarios of cosmological models are examined in this study. An arbitrary function, $f(Q,C)=Q+\alpha C^2$, has been taken into consideration, where $Q$ is the non-metricity scalar, $C$ is the boundary term denoted by $C=\ddot{R}-Q$, and $\alpha$ is the model parameter, for the action that is quadratic in $C$. The Hubble function $H(z)=H_0{[c_1{(1+z)}^n+c_2]}^{\frac{1}{2}}$, where $H_0$ is the current value of the Hubble constant and $n,c_1$ and $c_2$ are arbitrary parameters with $c_1+c_2=1$, has been used to examine the dark energy characteristics of the model. We discovered a transit phase expanding universe model that is both decelerated in the past and accelerated in the present, and we discovered that the dark energy equation of state (EoS) ${\omega }^{(de)}$ behaves as $(-1\le {\omega }^{(de)}<2)$. The Om diagnostic analysis reveals the quintessence behavior in the present and the cosmological constant scenario in the late-time universe. Finally, we calculated the universe’s current age, which was found to be quite similar to recent data.

This paper is an investigation of dark energy cosmological models in non-coincident gauge formulation of non-metricity gravity with boundary term. We have considered an arbitrary function $f(Q,C)=Q+\lambda C^m$, where $Q$ is the non-metricity scalar, $C$ is the boundary term derived by $C=\mathring{R}-Q$, and $\lambda ,m$ are the model parameters, to obtain the modified field equations from action. We have parameterized the Hubble function as $H(a)=k_0(a{(t)}^{-n}+k_1)$ with $n,k_0,k_1$ are arbitrary constants and $a(t)$ is the scale-factor depending upon cosmic time. We have compared this Hubble function with $H(z)$ datasets and obtained best fit values of model parameters using likelihood analysis. Using these best fit values of model parameters, we have done our result analysis and discussion with cosmological parameters viz effective equation of state parameter, energy density, energy conditions, deceleration parameter, om diagnostic analysis and age of the universe. We have found a transit phase universe model with effective EoS parameter $-1.18<{\omega }^{\mathrm{\text{eff}}}<-0.2$ over redshift $-1<z<3$.