Generalized Brans-Dicke cosmology, noether symmetries and quantization

Abstract

A generalized Brans-Dicke theory of gravitation is applied to investigate a cosmological model for primordial 
 universe that includes a self-interacting bosonic field as source. This model permits, initially, to consider an arbitrary $\omega$ function, not usual for BD formulations. The imposition of Noether symmetries conditions identifies a reduced space for the $\omega$ function. This model is shown to present a variety of behaviors consistent with a primordial era, depending on the parameters chosen. We find that the bosonic field is capable of promoting a transition from an initially accelerated to a decelerated regime. The self-interaction potential is also restricted by the Noether conditions, and can be interpreted as a vacuum energy contribution. The model also permits a quantization process, going through a hamiltonian formulation and recognizing the presence of cyclic variables. The Bohm approach shows as result a consistent model with a smooth classical limit as the universe leaves the Planck era.