Domain walls and CP violation with left right supersymmetry:implications for leptogenesis and electron EDM

Low scale leptogenesis scenarios are difficult to verify due to our inability to relate the parameters involved in the early universe processes with the low energy or collider observables. Here we show that one can in principle relate the parameters giving rise to the transient $CP$ violating phase involved in leptogenesis with those that can be deduced from the observation of electric dipole moment (EDM) of the electron. We work out the details of this in the context of the left right symmetric supersymmetric model (LRSUSY) which provides a strong connection between such parameters. In particular, we show that baryon asymmetry requirements imply the scale $M_{B-L}$ of $U(1)_{B-L}$ symmetry breaking to be larger than $10^{4.5}~\mathrm{GeV}$. Moreover the scale $M_R$ of $SU(2)_R$ symmetry breaking is tightly constrained to lie in a narrow band significantly below $M_{B-L}^2 / M_{EW}$. These are the most stringent constraints on the parameter space of LRSUSY model being considered.