Flat FLRW Universe in logarithmic symmetric teleparallel gravity with observational constraints

In this paper, we investigate the homogeneous and isotropic flat FLRW Universe in the logarithmic form of $f\left( Q\right)$ gravity, where $$ is the non-metricity scalar, specifically, $f\left( Q\right) =α+β\log \left( Q\right)$, where $α$ and $β$ are free model parameters. In this study, we consider a parametrization of the Hubble parameter as $H\left( z\right) =η\left[ (z+1)^{-γ}+1\right]$, where $γ$ and $η$ are model/free parameters which are constrained by an $R^{2}$-test from 57 points of the Hubble datasets in the redshift range $0.07<z<2.36$. Further, we investigate the physical properties of the model. We analyze the energy conditions to check the compatibility of the model. We found the SEC is violated for the logarithmic form of $f\left( Q\right)$ gravity due to the reality that the Universe in an accelerating phase. Finally, we discuss some important cosmological parameters in this context to compare our model with dark energy models such as jerk parameter and statefinder parameters.

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