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.

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 $-1<z<3$.