A qualitative and numerical analysis of cosmological models based on assymetric scalar doublet: classical + phantom scalar field. I. A case of minimally interacting scalar fields: the qualitative analysis

Abstract: The paper provides a qualitative and numerical analysis-based investigation of cosmological models founded on an asymmetrical scalar doublet comprising of a classical and a phantom scalar fields. Presence of a phantom scalar field allows one to consider also classical scalar fields with attraction of like-charged particles which significantly extends a diversity of cosmological models' behaviours. It is shown that a cosmological model based on an asymmetric scalar doublet in the case of minimal interaction has 9 singular points 2 of which are attractive and the rest are non-stable saddle ones. It is also shown that a presence of even essentially weak phantom field significantly changes the dynamics of a cosmological model.