This work investigates the cosmological implications of the Extended Bose–Einstein Condensate (EBEC) equation of state within the framework of f(Q, C) gravity, aiming to provide deeper insight into the nature of dark matter and dark energy. The EBEC model, characterized by the equation of state \(p = \alpha \rho + \beta \rho ^2\) , unifies classical dark matter with its quantum ground state properties. A linear model \(f(Q,C) = -\psi \left( \frac{Q}{Q_0}\right) + \delta C\) (Model 1) and a nonlinear model \(f(Q,C) = -\psi \left( \frac{Q}{Q_0}\right) ^2 + \delta C\) (Model 2) are investigated. We constrain the parameters of both models with CC, BAO and Pantheon supernova datasets via MCMC techniques. The best-fit values for \(H_0\) , \(\eta\) , and \(\beta\) for each model lie within observational bounds. Our analysis reveals a consistent late-time transition from deceleration to acceleration, with the present-day equation of state parameter \(\omega _0\) asymptotically approaching \(-1\) , resembling a cosmological constant. The SEC is violated in both models across all redshifts, indicating the presence of repulsive gravity, while the other conditions are preserved, ensuring physical viability. The evolution of the statefinder parameters shows trajectories passing through the \(\Lambda\) CDM fixed point \((r=1, s=0)\) , transitioning from a quintessence-like phase to a future phantom regime. Both models exhibit stable behavior with a sound speed squared \(0< c_s^2 < 1\) throughout cosmic history. The estimated ages of the Universe from the datasets are approximately 13.47–13.57 billion years for Model 1 and 13.49–13.59 billion years for Model 2. These results demonstrate that both linear and nonlinear forms of the f(Q, C) gravity model, when coupled with EBEC dark matter, offer viable and physically consistent descriptions of the Universe’s late-time accelerated expansion.
