Quantum cosmological perfect fluid models in Einstein aether theory

The possibility of constructing a consistent quantum theory of gravitation has motivated the recent interest in gravitational theories that break Lorentz invariance, as it is the case of Einstein aether theory. In this work, we employ Schutz variational formalism to obtain a quantum cosmological Einstein aether model for a spatially flat Universe filled with a barotropic fluid with equation of state p=αρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p=\alpha \rho $$\end{document}. Solutions to the Wheeler–DeWitt equation are obtained by the superposition of stationary quantum states, yielding finite-norm wave packets. The behavior of the scale factor is studied from the point of view of the many-worlds and of the de Broglie–Bohm interpretations of quantum mechanics, indicating non-singular solutions for α<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha < 1$$\end{document}.