Probing dark energy properties in f(Q, C) gravity with FLRW cosmological models

This study delves into the cosmological implications of the f(Q, C) modified gravity framework within the context of the Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime which offers a dynamic alternative to the standard Lambda CDM cosmology. Here, we define the transit form of Hubble's parameter to explain several geometrical and physical aspects. The chosen parametric form of the Hubble parameter represents a smooth transition from the decelerating early universe to the accelerating present and late-time evolution. Employing observational datasets such as the Hubble parameter, Type Ia supernovae, Baryon Acoustic Oscillations (BAOs), and Standard Candles (SC), we constrain the model parameters using the Markov Chain Monte Carlo (MCMC) method. The isotropic pressure, energy density, equation of state parameter, and energy conditions were analyzed to explore the physical viability of the f(Q, C) framework. The results highlight the model's ability to replicate key cosmological behaviors, including the accelerated expansion driven by dark energy. Also, the results indicate that the f(Q, C) model can effectively reproduce the late-time accelerated expansion of the universe while offering a slightly different dynamical evolution of the equation of state parameter. Additionally, statistical model selection criteria, such as the Akaike Information Criterion (AIC), suggest that the viability of f(Q, C) gravity is comparable to that of Lambda CDM, making it a promising alternative for explaining cosmic acceleration.