Exploring the Dynamics of Dark Energy in \(\boldsymbol{f(Q,C)}\) Gravity: A Comprehensive Analysis Using Cosmological Datasets

We study the \(f(Q,C)\) gravity model by finding a power-law solution for the Hubble parameter \(H(z)=H_{0}(1+z)^{{3}/{2n}}\) and examine its consequences using a variety of cosmological datasets. Our approach involves the fitting of the model parameters to datasets from Hubble, BAO and Phantom that are in good agreement with observations. Upon analyzing the energy density \(\rho(z)\), we discover that it provides evidence for a dynamic dark energy theory. The \(Om(z)\) diagnostic and the statefinder parameters \(r\) and \(s\) show the behaviours that is compatible with quintessence models. According to our findings, the \(f(Q,C)\) gravity model offers a feasible substitute for the conventional \(\Lambda\)CDM model and offer a valuable understanding into the dynamic characteristics of dark energy and cosmic expansion.