Reconstruction of Tsallis Holographic Dark Energy via Modified Non-Metric Gravity: An $f(Q,C)$ Approach

In the current research, we have reported the Tsallis Holographic Dark Energy (THDE) ($\mathit{\text{JCAP}}$, 2018(12), p.012.) model reconstructed within the framework of $f(Q,C)$ gravity ($\mathit{\text{JCAP}}$, 2024(03), p.050.), combining entropy-based dark energy models with geometrically motivated modified gravity to explain late-time cosmic acceleration. The reconstructed model is found to exhibit significant sensitivity to the parameter space $(H_0,a_0,n,\delta ,\zeta ,r_d)$ and the initial conditions. The evolution of the equation of state and deceleration parameters is found to be highly dependent on these parameters. A comprehensive Markov Chain Monte Carlo analysis using observational datasets comprising {CC+Pantheon${}^{+}$+DESI DR2} was performed, yielding best-fit values that demonstrate strong consistency with observational data, which is further validated for its consistency through the computation of the age of the Universe. The evolution of the jerk and snap parameters is examined and compared with the $\mathrm{\Lambda }$CDM prediction. Statefinder diagnostics, through the evolutionary trajectories of the pairs $(r,s)$ and $(r,q)$ are derived and indicate that the model passes through the $\mathrm{\Lambda }$CDM fixed point and the physical viability of the model is further consolidated through analysis of the four energy conditions.