Аннотация
Abstract In this work, we study the Barrow Holographic Dark Energy (BHDE) model (Phys Rev D 102:123525, 2020), which is based on Barrow’s modification of entropy. We show that this model is a special case of the more general Nojiri–Odintsov HDE (NO-HDE) framework (Eur Phys J C 77:528, 2017). In the same way, the Granda–Oliveros (GO) cutoff also appears as a particular case of the NO cutoff. After this, we reconstruct the dynamics of BHDE using a k-essence scalar field, which provides a field theory picture of its evolution. The results show how the Barrow deformation parameter and the infrared cutoff affect the kinetic term and the behaviour of the scalar field. Further, we test the thermodynamic consistency of the model by checking the generalized second law on cosmological horizons. Overall, the study confirms that both BHDE and the GO cutoff can be understood as limits of the NO-HDE framework, and that they are consistent with scalar field theory and the principles of thermodynamics. Also we confront the reconstructed BHDE–k-essence model with late-time cosmological data from cosmic chronometers and baryon acoustic oscillations. The features derived in the study the models under as viable models to explain the late-time cosmic acceleration.