Eur. Phys. J. Plus (2021) 136: 1130
https://doi.org/10.1140/epjp/s13360-021-02125-0

Regular Article

Einstein-æther scalar–tensor cosmology

¹ Institute of Systems Science, Durban University of Technology, 4000, Durban, South Africa
² Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, 5090000, Valdivia, Chile
³ Departamento de Matemáticas, Universidad Católica del Norte, Avda. Angamos 0610, 1280, Casilla, Antofagasta, Chile

^b genly.leon@ucn.cl

Received: 1 August 2021
Accepted: 27 October 2021
Published online: 11 November 2021

Abstract

We propose an Einstein-æther scalar–tensor cosmological model. In particular, in the scalar–tensor Action Integral, we introduce the æther field with æther coefficients to be functions of the scalar field. This cosmological model extends previous studies on Lorentz-violating theories. For a spatially flat Friedmann–Lemaître–Robertson–Walker background space, we write the field equations which are of second order with dynamical variables the scale factor and the scalar field. The physical evolution of the field equations depends upon three unknown functions which are related to the scalar–tensor coupling function, the scalar field potential, and the æther coefficient functions. We investigate the existence of analytic solutions for the field equations and the integrability properties according to the existence of linear in the momentum conservation laws. We define a new set of variables in which the dynamical evolution depends only upon the scalar field potential. Furthermore, the asymptotic behavior and the cosmological history are investigated where we find that the theory provides inflationary eras similar to that of scalar–tensor theory but with Lorentz-violating terms provided by the æther field. Finally, in the new variables, we found that the field equations are integrable due to the existence of nonlocal conservation laws for arbitrary functional forms of the three free functions.