Cosmic acceleration and crossing of w=-1 barrier in non-local Cubic   Superstring Field Theory model
  We show that the late time rolling of the Cubic Superstring Field Theory (CSSFT) non-local tachyon in the FRW Universe leads to a cosmic acceleration with a periodic crossing of the w=-1 barrier. An asymptotic solution for the tachyon and Hubble parameter by linearizing the non-local equations of motion is constructed explicitly. For a small Hubble parameter the period of oscillations is a number entirely defined by the parameters of the CSSFT action. 
I.Ya. Aref'eva and A.S. Koshelev