Integrable cosmological models with nonminimally coupled scalar fields
Abstract
We obtain general solutions for some flat Friedmann universes filled with a scalar field in induced gravity models and models including the HilbertEinstein curvature term plus a scalar field conformally coupled to gravity. As is well known, these models are connected to minimally coupled models through the combination of a conformal transformation and a transformation of the scalar field. The explicit forms of the selfinteraction potentials for six exactly solvable models are presented here. We obtain the general solution for one of the integrable models, namely, the induced gravity model with a powerlaw potential for the selfinteraction of the scalar field. We argue that although being mathematically in a onetoone correspondence with the solutions in the minimally coupled models, the solutions in the corresponding nonminimally coupled models are physically different. This is because the cosmological evolutions seen by an internal observer connected with the cosmic time can be quite different. The study of a few induced gravity models with particular potentials gives us an explicit example of such a difference.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 May 2014
 DOI:
 10.1088/02649381/31/10/105003
 arXiv:
 arXiv:1312.3540
 Bibcode:
 2014CQGra..31j5003K
 Keywords:

 98.80.Jk;
 04.50.Kd;
 04.20.Jb;
 cosmology;
 integrable models;
 scalar fields;
 High Energy Physics  Theory;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 20 pages, v3: references added, accepted for publication in CQG