Spontaneous R-parity breaking, Left-Right Symmetry and Consistent Cosmology with Transitory Domain Walls

Domain wall formation is quite generic in spontaneous Left-Right parity (D-parity) breaking models. Since they are in conflict with cosmology, we need some mechanisms to remove them. Planck scale suppressed effects have been considered to be quite successful for this purpose. We study this possibility in Minimal Supersymmetric Left-Right (SUSYLR) model originally proposed by Kuchimanchi et al \cite{Kuchimanchi:1993jg} where both D-parity and R-parity $(R_p=(-1{)}^{3(B-L)+2s})$ are spontaneously broken. We find that Planck scale suppressed terms allowed for the specific particle content of this model can successfully remove the domain walls provided the D-parity breaking scale is relatively low $(\le {10}^5-{10}^7\text{GeV})$. However, demanding this theory to be part of a grand unified theory such as SO(10) forces the D-parity breaking scale to be very high $(\ge {10}^{14}\text{GeV})$ and hence is in conflict with the constraint from domain wall removal. We also find another class of R-parity violating SUSYLR models where both these constraints can be simultaneously satisfied.