Note on nonsingular Einstein-Aether cosmologies

An effective Lagrangian approach, based on an extended Einstein-Aether (EA) model, is proposed. This model is presented as an alternative to GR and mimetic gravity models in order to deal with the big bang cosmological singularity issue. In particular, working on non flat Friedmann-Lemaitre-Robertson-Walker (FLRW) space-time, a generalized Friedmann equation is derived, and it is shown that, for a suitable choice of the action within the extended EA theory, a regular bounce solution is present, generalizing the bounce solution obtained in quantum loop cosmology (QLC) in the flat case. Furthermore, perturbation theory of the extended model is investigated, and the main perturbation quantities are evaluated and the conditions to avoid physical (superluminarity) and mathematical instabilities are discussed. Finally, the static spherically symmetric (SSS) case is also investigated. It is found that, with the same action proposed for the FLRW space-time, a Schwarschild like solution with a correction is obtained.