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Interdependence between integrable cosmological models with minimal and non-minimal coupling. (English) Zbl 1331.83121

Summary: We consider the relation between exact solutions of cosmological models having minimally and non-minimally coupled scalar fields. This is done for a particular class of solvable models which, in the Einstein frame, have potentials depending on hyperbolic functions and in the Jordan frame, where the non-minimal coupling is conformal, possess a relatively simple dynamics. We show that a particular model in this class can be generalized to the cases of closed and open Friedmann universes and still exhibits a simple dynamics. Further we illustrate the conditions for the existences of bounces in some sub-classes of the set of integrable models we have considered.

MSC:

83F05 Relativistic cosmology
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C15 Exact solutions to problems in general relativity and gravitational theory
83C75 Space-time singularities, cosmic censorship, etc.
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