Kantowski-Sachs and Bianchi type models with a general non-canonical scalar field

The paper deals with spatially homogeneous and anisotropic Kantowski-Sachs and Bianchi universes with a general non-canonical scalar field with the Lagrangian L = F(X) − Ω(ϕ), where X=12ϕiϕi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X = \frac{1}{2}{\phi _i}{\phi ^i}$$\end{document}. We discuss a general non-canonical scalar field in three different cosmologies: (i) cosmology with a constant potential, Ω(ϕ) = Ω0 = const, (ii) cosmology with a constant equation-of-state parameter, i.e., γϕ = const, and (iii) cosmology with a constant speed of sound, i.e., cs2 = const. For a constant potential, we have shown that the k-essence Lagrangian and the Lagrangian of the present model are equivalent. Dissipation of anisotropy, when the universe is filled with a general non-canonical scalar field, is investigated. The existence of an average bounce in Kantowski-Sachs and locally rotationally symmetric Bianchi-I and Bianchi-III models is discussed in detail.