Interdependence between integrable cosmological models with minimal and non-minimal coupling

Abstract

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 nonminimal 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.

A note on a mimetic scalar–tensor cosmological model

“…Of course, in GR, one may make use of the Friedmann equation to arrive directly at the explicit solution for a(t), a textbook result. In the presence of a scalar field, things are not so simple, and, in general, it is not easy to find exact solutions (see, for example [3,4]). Furthermore, in the standard cosmological model, Dark Matter and Dark energy issues are still under investigation, since one has no clue what they are.…”

General analytic solutions of scalar field cosmology with arbitrary potential

“…We are interested in the analytic solutions of that cosmological model. Exact closed-form solutions without matter term or with a dust fluid can be found in [27][28][29][30][31][32][33][34][35][36][37] and in the case of a non-minimal coupling in [38][39][40], while for non-spatially flat FLRW spacetimes some exact solutions are contained in [41][42][43]. Further analytic solutions for a scalar field model with the presence of a perfect fluid have been presented in [44][45][46][47][48].…”

Multi-fluid cosmology in Einstein gravity: analytical solutions

“…There are other methods to find analytical cosmological solutions with nonminimally coupled models scalar fields [229] and to connect integrable cosmologies in the Jordan and the Einstein frames [230,231].…”