Tachyon potentials from a supersymmetric FRW model
  Considering that the effective theory of closed string tachyons can have worldsheet supersymmetry, as shown by Vafa, we study a worldline supersymmetric action in a FRW background, whose superpotential originates a tachyon scalar potential. There are such potentials with spontaneously broken supersymmetry at the instability and supersymmetric after tachyon condensation. Furthermore, given a tachyonic potential, the superpotential can be computed by a power series ansatz and has a free parameter which can be chosen such that complex solutions become real. 
G. Garc\'ia-Jim\'enez, C. Ram\'irez and V. V\'azquez-B\'aez
hep-th gr-qc