ИСТИНА

We explore dynamics of cosmological models with a non-minimally coupled scalar field evolving on a spatially flat Friedmann-Lemaitre-Robertson-Walker background. We propose a method to obtain integrable cosmological models with non-minimally coupled scalar fields. These models are connected to integrable minimally coupled models through the combination of a conformal transformation and a transformation of the scalar field. We present 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. The knowledge of asymptotic solutions and global qualitative analysis allow us to describe important properties of solutions in non-integrable cases. The influence of the cosmological constant to the global features of dynamics is also studied.