Einstein-æther scalar–tensor cosmology

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