http://arxiv.org/abs/1312.3540
We construct general solutions for 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. The corresponding models are connected with 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 argue that although being mathematically in a one-to-one correspondence with the solutions in the minimally coupled models, the solutions in the respective 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. We give an explicit example of such a difference.
Tue, 17 Dec 13
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