Logarithmic \({\varvec{f}}({\varvec{Q}})\) gravity with parametrization of deceleration parameter and energy conditions

Abstract

This research focuses on parametrization of deceleration parameter within the structure of modified symmetric teleparallel gravity or \(f\left(Q\right)\) gravity, where \(Q\) represents the nonmetricity scalar. To explore evolutionary timeline of the Universe, we considered the logarithmic form: \(f\left(Q\right)=m+n \text\,{\rm{{ln}}}(Q)\), where \(m\) and \(n\) are constants. In this context, we utilize a particular form of deceleration parameter given by \(q\left(z\right)=\frac{1}{2}+\frac{{q}_{1}z+{q}_{2}}{{(1+z)}^{2}},\) where \({q}_{1}\), \({q}_{2}\) and redshift, \(z\) are the parameters. This form allows a transition from a decelerating phase to an accelerating phase. Solution for the Hubble parameter is derived using the given parametric form of \(q\), which is then applied to the Friedmann equations. Following this, we estimated the model parameters’ best-fit values by using 115 supernovae Ia data points and Planck Collaboration (2018). We also focus on testing energy conditions in the context of cosmological acceleration. Moreover, we analysed the evolution of density, pressure, equation of state (EoS) parameter and Om(z) diagnostics to understand accelerated expansion phase of the Universe.