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.
Integrable cosmological models with non-minimally coupled scalar fields / A. Kamenchtchik; E. Pozdeeva; A. Tronconi; G. Venturi; S. Vernov. - In: CLASSICAL AND QUANTUM GRAVITY. - ISSN 0264-9381. - STAMPA. - 31:(2014), pp. 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.