  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.
