ИСТИНА

We consider cosmological models with an arbitrary number of scalar fields nonminimally coupled to gravity and construct new integrable cosmological models. In the constructed models, the Ricci scalar is an integral of motion, irrespectively of the type of metric. In the case of two fields, we construct integrable chiral cosmological models with potentials represented in terms of hyperbolic functions using the conformal transformation of the metric. We obtain the general solutions in the spatially flat, open and closed Friedmann universes and the corresponding integrals of motion. The obtained general solutions can be written in terms of the Jacobi elliptic functions of the conformal time.