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 $t(z)=\frac{m{t}_0}{l}g(z)$, where $g(z)=\mathrm{\text{Lambert}}W\left[\right.\frac{l}{m}{e}^{\frac{l-ln(1+z)}{m}}\left]\right.$, $m$ 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.

该论文介绍了 Barrow [The area of​​ a rough black hole, Phys. 莱特。B  808 (2020) 135643] 最近在一个各向异性的比安奇 I 型宇宙的框架内$F(问)$对称远平行引力，其中非公制标量$问$负责引力相互作用。我们考虑两种情况：无压力暗物质和巴罗全息暗能量的相互作用和非相互作用模型，通过求解$F(问)$对称远平行场方程。为了找到场方程的精确解，我们假设时间-红移关系服从 Lambert 函数分布为$吨(z)=\frac{米{吨}_0}{升}G(z)$， 在哪里$G(z)=\mathrm{\text{兰伯特}}W\left[\right.\frac{升}{米}{\mathrm{电子}}^{\frac{升-在(\mathrm{1个}+z)}{米}}\left]\right.$,$米$和$升$是非负常数和${吨}_0$代表宇宙的年龄。此外，我们还讨论了几个宇宙学参数，例如能量密度、状态方程 (EoS) 和偏度参数、平方声速和$({\omega }_{乙}-{\omega }_{乙}^{{}^{‘}})$飞机。最后，我们发现 Lambert 函数分布的减速参数 (DP) 的值为$q_{(z=0)}=-0.\mathrm{4个}\mathrm{5个}$和$q_{(z=-\mathrm{1个})}=-\mathrm{1个}$这与最近的观测数据一致，即 DP 随宇宙时间从初始减速到后期加速演化。