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.

A. Kamenchtchik, E. Pozdeeva, A. Tronconi, G. Venturi, S. Vernov (2014). Integrable cosmological models with non-minimally coupled scalar fields. CLASSICAL AND QUANTUM GRAVITY, 31, 105003-105003 [10.1088/0264-9381/31/10/105003].

Integrable cosmological models with non-minimally coupled scalar fields

KAMENCHTCHIK, ALEXANDR;TRONCONI, ALESSANDRO;VENTURI, GIOVANNI;
2014

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.
2014
A. Kamenchtchik, E. Pozdeeva, A. Tronconi, G. Venturi, S. Vernov (2014). Integrable cosmological models with non-minimally coupled scalar fields. CLASSICAL AND QUANTUM GRAVITY, 31, 105003-105003 [10.1088/0264-9381/31/10/105003].
A. Kamenchtchik; E. Pozdeeva; A. Tronconi; G. Venturi; S. Vernov
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/278513
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