Journal
CLASSICAL AND QUANTUM GRAVITY
Volume 31, Issue 10, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/0264-9381/31/10/105003
Keywords
cosmology; integrable models; scalar fields
Categories
Funding
- RFBR [14-01-00707, 12-02-31109, 14-02-00894]
- Russian Ministry of Education and Science [NSh-3920.2012.2, NSh-3042.2014.2]
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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.
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