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

TL;DR

This paper investigates Barrow holographic dark energy within $f(Q)$ symmetric teleparallel gravity in an anisotropic universe, deriving exact solutions using Lambert function distribution and analyzing cosmological parameters to match observational data.

Contribution

It introduces a novel Lambert function approach to solve $f(Q)$ gravity field equations with holographic dark energy, considering anisotropic models and interaction effects.

Findings

Deceleration parameter evolves from positive to negative, indicating transition from deceleration to acceleration.

Model parameters are consistent with current observational data.

Exact solutions for anisotropic $f(Q)$ gravity with holographic dark energy are obtained.

Abstract

The paper presents Barrow holographic dark energy (infrared cut-off is the Hubble horizon) suggested by Barrow recently (Physics Letters B 808 (2020): 135643) in an anisotropic Bianchi type-I Universe within the framework of $% f\left( Q\right) $ 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\left( Q\right) $ 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\left( z\right) =\frac{mt_{0}}{l}g\left( z\right) $, where $g\left( z\right) =LambertW\left[ \frac{l}{m}e^{\frac{l-\ln \left( 1+z\right) }{m}}\right] $, $m$ 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 $(\omega _{B}-\omega _{B}^{^{\prime }})$ 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.