Barrow holographic dark energy in f(Q,Lm) gravity: A dynamical system perspective

In this work, we focus on the study of the accelerated expansion of the Universe by investigating the Barrow Holographic Dark Energy (BHDE) model within the framework of [Formula: see text] gravity by focusing on the specific form [Formula: see text]. Employing a dynamical system approach, we analyze both non-interacting and interacting scenarios to identify critical points corresponding to distinct phases of the Universe’s evolution, including matter domination, radiation domination and dark energy-driven accelerated expansion. Our findings reveal two stable critical points in the non-interacting case and three stable critical points in the interacting case which indicates the transitions to stable phases dominated by BHDE. These results address the problem of modeling the evolution of the Universe’s dynamics, particularly the nature of dark energy. The phase plots demonstrate the Universe’s progression toward these stable points, where the deceleration parameter [Formula: see text] and the EoS parameter [Formula: see text] remain negative, which implies the accelerated expansion of the Universe. The present values [Formula: see text] and [Formula: see text] (non-interacting) and [Formula: see text] and [Formula: see text] (interacting) further support the current accelerated expansion of the Universe. Additionally, comparisons with the [Formula: see text] Hubble datasets and [Formula: see text] Pantheon Supernovae datasets validate the model’s predictions by reinforcing the viability of BHDE as a model which is comparable to the standard [Formula: see text]CDM model and its potential to provide deeper insights into the accelerating Universe.