ИСТИНА

Cosmological models with scalar fields play an important role in the description of the global evolution of the Universe. Many inflationary and dark energy models can be formulated as models with scalar fields that are possibly non-minimally coupled to gravity. In spite of the great success of numerical simulations and approximation schemes, the exact analytical solutions of the Einstein equations are always useful. At the same time, the number of integrable cosmological models is rather limited, and most of the results of the exact integration are connected with cosmological models in the FLRW metric with scalar fields minimally coupled to gravity. We study integrable models in the FLRW and Bianchi I metrics with scalar fields minimally and non-minimally coupled with gravity and the correspondence between their general solutions. Our goal is to construct new sets of integrable cosmological models that include models with both minimal and non-minimal coupling.