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

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 f(Q) symmetric teleparallel gravity, where the non-metricity scalar Q 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 f(Q) 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 t(z) = mt(0)/l g(z), where g(z) = LambertW [l/me(l-ln(1+z)/m)] , m and l are non-negative constants and t(0) 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 (omega(B) - omega(B)') plane. Finally, we found the values of the deceleration parameter (DP) for the Lambert function distribution as q((z=0)) = -0.45 and q((z=-1)) - -1 which are consistent with recent observational data, i.e. DP evolves with cosmic time from initial deceleration to late-time acceleration.