On holographic dark energy in non-isotropic Universe with Brans-Dicke theory

A spatially homogeneous and anisotropic Bianchi type I Universe has been studied with the interacting holographic dark energy (HDE) in the framework of Brans-Dicke theory. At first, we obtain the equation of state parameter, the deceleration parameter and the evolution equation of the interacting HDE in BD theory. We find that, in this case, ωΛ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\omega_{\varLambda}$\end{document} can cross the phantom line (ωΛ>−1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\omega_{\varLambda}>-1$\end{document}) and eventually the Universe approaches a de-Sitter phase of expansion (ωΛ→−1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\omega_{\varLambda}\rightarrow-1$\end{document}). Then, we extend our study to the case of stability of the interacting HDE in BI Universe according to BD theory. In case of we find that the squared sound speed of the interacting HDE is either positive or negative. This implies that the interacting HDE in BD theory can lead to a stable Universe favored by observations at the present time in an anisotropic Universe.