Symmetry non-restoration via order 10−10 B and L asymmetries

It has been observed that a large lepton asymmetry, nL/s≈0.1, can prevent the Higgs expectation value from going to zero at high temperature, resulting in the non-restoration of the SU(2)×U(1) gauge symmetry and other symmetries. This could allow for the elimination of domain walls and other dangerous topological defects. Here we show that if the reheating temperature after inflation, TR, is sufficiently low then symmetry non-restoration will occur with an asymmetry of the order of the observed baryon asymmetry, nB/s≈10−10. For this to occur TR≲1 GeV is necessary. Remarkably, this happens to be the reheating temperature expected in Affleck–Dine baryogenesis along a d=6 flat direction of the MSSM. As an example, we show that this can neatly solve the Z3 domain wall problem of the NMSSM.