The anisotropic string cosmological model of Bianchi type I in general relativity

We study the maximum symmetric, Anisotropic, inhomogeneity string theory of Bianchi type I in general relativity. We assume Einstein string space metric depends on two variable expansion, Our four directions and these variable functions are related to the condition, a[x,t]=[b(x,t)]n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a[x,t] = [b(x,t)]<^>{n}$$\end{document} where c[x,t]=h(x)xk(t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c[x,t] = h(x) \times k(t)$$\end{document} & b[x,t]=f(x)xg(t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b[x,t] = f(x) \times g(t)$$\end{document} metric potential and shear tension are directly proportional to scalar expansion, Our analysis carefully incorporates a condition that links these variable functions to find the deterministic solution. The higher and varied dimensions models' geometrical and physical characteristics are also looked at.