Cosmological Constraint on the Scale of the Supersymmetric Singlet Majoron

In a SUSY theory with a spontaneously broken global symmetry, G, if the scale of SUSY breaking, $M_s$ is smaller than the scale $M_G$ of the global symmetry, the Nambu-Goldstone boson, $\chi$ is accompanied by two massive superpartners ( a fermionic, $\Psi_\chi$ and a scalar $\sigma_\chi$) with mass of order $M_s$. Cosmological considerations imply stringent constraints on the couplings of $\Psi_\chi$ and $\sigma_\chi$. Application of these considerations to the supersymmetric singlet Majoron model leads to an upper limit on the scale $V_{BL}$ of global $U(1)_{B-L}$ symmetry to be less than $10^4 GeV$, for resonable values of parameters in the theory.