Integrable cosmological models with non-minimally coupled scalar fields

Understand

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.