Understanding the nature of dark energy remains one of the central challenges in modern cosmology, motivating the exploration of modified gravity theories and quantum gravitational corrections. In this work, we explore the reconstruction of f(Q, T) gravity within the Barrow Holographic Dark Energy (BHDE) framework. Motivated by quantum gravitational effects, BHDE modifies the standard holographic dark energy via a deformed entropy-area relation characterized by the Barrow parameter δ. Adopting the form f(Q, T) = Q + h(T), we reconstruct the theory using three infrared cutoffs: the Hubble horizon, the future event horizon, and the Granda-Oliveros cutoff. The function h(T) exhibits distinct behaviors: power law, logarithmic, or exponential growth, depending on the cutoff and the Barrow parameter δ. Furthermore, we analyze the evolution of the effective Newton’s constant to assess the viability of the reconstructed Q + h(T) model and its deviation from general relativity. The resulting models account for the late-time acceleration of the universe and allow for quintessence or phantom-like dynamics (dependence on δ), offering a viable framework for exploring dark energy and potential quantum gravity effects. In addition, the condition of the effective Newton’s constant and the dark energy equation of state offer qualitative indications that our models may have the potential to alleviate the existing H 0 and S 8 tensions.
Mohanty et al. (Thu,) studied this question.