Construction of exact solutions in cosmological models with phantom scalar fields
We explore a possibility for the Universe to cross the $w=-1$ cosmological constant barrier for the dark energy state parameter. We construct an exact analytic solution to the Friedman equations with a string inspired scalar matter. To find such solutions the method of superpotential, developed in the five-dimensional brane-world scenario is used. A local effective model contains one phantom component and one usual scalar field with a polynomial interaction. To understand cosmological properties of such system we study a few models with the same scalar fields but with modified interactions. These modifications admit polynomial superpotentials. We find restrictions on these interactions under which it is possible to reach $w=-1$ from below at large time. Explicit solutions with the dark energy state parameter crossing/non-crossing the barrier $w=-1$ are presented.