Parameterized Deceleration in f(Q,C) Gravity: A Logarithmic Approach

Abstract

This study explores a novel logarithmic parameterization of the deceleration parameter within the $f(Q,C)$ gravity framework, incorporating a nonlinear functional form $f(Q,C)={\gamma }_1{Q}^n+{\gamma }_{2}C$, where $Q$ and $C$ denote the nonmetricity scalar and boundary term respectively and $n>1$. This approach provides a distinctive perspective on the accelerated expansion of the universe without resorting to exotic fields. Using Observational Hubble Data ($OHD$) measurement and the $Pantheon+SH0ES$ Type Ia supernovae dataset, the model parameters were restricted by a ${\chi }^2$ minimization technique. The analysis reveals a transition from deceleration to acceleration in the expansion history of the universe, with transition redshifts $z_t\approx 0.98$ ($OHD$) and $z_t\approx 0.76$ ($Pantheon+SH0ES$). The model demonstrates consistency with observations, offering insights into the dynamics of dark energy and alternative gravity theories while effectively modeling cosmic evolution across epochs.