Abstract
Understanding the accelerating expansion of the universe remains one of the foremost challenges in modern cosmology. This study investigates Barrow Holographic Dark Energy (BHDE), a model inspired by quantum gravitational corrections, within the framework of \(f(Q,C)\) gravity. This extension of symmetric teleparallel gravity incorporates the non-metricity scalar \(Q\) and the boundary term \(C\), enabling a deeper exploration of cosmic dynamics without relying on a cosmological constant or exotic matter. The BHDE model is analyzed under a flat Friedmann-Robertson-Walker (FRW) metric, focusing on key cosmological parameters such as energy density, isotropic pressure, the equation of state (EoS) parameter, stability conditions and the energy conditions. The results demonstrate that the EoS parameter transitions from matter-like behavior (\(z > 0\)) to negative values at \(z = 0\), indicating the dominance of dark energy and its role in the universe's accelerated expansion. As \(z\) approaches \(-1\), the EoS parameter asymptotically converges to \(-1\), aligning with the \(Λ\)CDM model. This work underscores the potential of the BHDE model in \(f(Q,C)\) gravity as a comprehensive framework for studying cosmic acceleration. By incorporating Barrow entropy and addressing the interplay between non-metricity and boundary terms, the model provides a dynamic approach to explaining dark energy.