We study general constraints on spontaneous R-symmetry breaking models. Firstly, we investigate a cosmic string associated with the R-symmetry breaking which can be viewed as a tube-like domain wall with a winding number interpolating a false vacuum and a true vacuum. Such string causes inhomogeneous decay of the false vacuum to the true vacuum via rapid expansion of the radius of the tube and hence its formation would be inconsistent with the present Universe. Secondary, we show general constraints coming from the cosmological effects of the pseudo Nambu-Goldstone bosons, R-axions. They are substantially produced in the early Universe and may cause several cosmological problems.
References: arXiv:1211.5662 [hep-ph], 1211.7237 [hep-th], 1303.2740 [hep-ph], 1304.0623 [hep-ph].