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

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 \(n \geq 1\). This approach provides a distinctive perspective on the universe’s accelerated expansion without resorting to exotic fields. Using observational data from Hubble measurements (\(OHD\)) and the \(Pantheon + SH0ES\) Type Ia supernovae dataset, the model parameters were constrained through a \(\chi^2\) minimization technique. The analysis reveals a transition from deceleration to acceleration in the universe’s expansion history, with the 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.