Integrable cosmological models with non-minimally 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 Hilbert-Einstein 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 self-interaction 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 power-law potential for the self-interaction of the scalar field. We argue that although being mathematically in a one-to-one correspondence with the solutions in the minimally coupled models, the solutions in the corresponding non-minimally 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:
- 10.1088/0264-9381/31/10/105003
- 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
- E-Print:
- 20 pages, v3: references added, accepted for publication in CQG