  We study the cosmology of two versions of supersymmetric Left-Right symmetric
model. The scale of the $B-L$ symmetry breaking in these models is naturally
low, $10^4 - 10^6$ GeV. Spontaneous breakdown of parity is accompanied by a
first order phase transition. We simulate the domain walls of the phase
transition and show that they provide requisite conditions, specifically, $CP$
violating phase needed for leptogenesis. Additionally soft resonant
leptogenesis is conditionally viable in the two models considered. Some of the
parameters in the soft supersymmetry breaking terms are shown to be constrained
from these considerations. It is argued that the models may be testable in
upcoming collider and cosmology experiments.
