Crossing of the w=-1 Barrier by D3-brane Dark Energy Model
  We explore a possibility for the Universe to cross the w=-1 cosmological constant barrier for the dark energy state parameter. We consider the Universe as a slowly decaying D3-brane. The D3-brane dynamics is approximately described by a nonlocal string tachyon interaction and a back reaction of gravity is incorporated in the closed string tachyon dynamics. In a local effective approximation this model contains one phantom component and one usual field with a simple polynomial interaction. To understand cosmological properties of this system we study toy 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 at large time are presented. 
I.Ya. Aref'eva, A.S. Koshelev and S.Yu. Vernov