Barrow holographic dark energy models in f(Q) symmetric teleparallel gravity with Lambert function distribution

Abstract

The paper presents Barrow holographic dark energy (infrared cut-off is the Hubble horizon) suggested by Barrow [The area of a rough black hole, Phys. Lett. B 808 (2020) 135643] recently in an anisotropic Bianchi type-I Universe within the framework of [Formula: see text] symmetric teleparallel gravity, where the non-metricity scalar [Formula: see text] is responsible for the gravitational interaction. We consider two cases: Interacting and non-interacting models of pressureless dark matter and Barrow holographic dark energy by solving [Formula: see text] symmetric teleparallel field equations. To find the exact solutions of the field equations, we assume that the time-redshift relation follows a Lambert function distribution as [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are non-negative constants and [Formula: see text] represents the age of the Universe. Moreover, we discuss several cosmological parameters such as energy density, equation of state (EoS) and skewness parameters, squared sound speed, and [Formula: see text] plane. Finally, we found the values of the deceleration parameter (DP) for the Lambert function distribution as [Formula: see text] and [Formula: see text] which are consistent with recent observational data, i.e. DP evolves with cosmic time from initial deceleration to late-time acceleration.