Abstract

We propose an Einstein-AE ther scalar-tensor cosmological model. In particular, in the scalar-tensor Action Integral, we introduce the AE ther field with AE ther coefficients to be functions of the scalar field. This cosmological model extends previous studies on Lorentz-violating theories. For a spatially flat Friedmann-Lemaitre-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 AE ther 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 AE ther 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.