Gravitino decay into a neutrino and a sneutrino in the inflationary universe

We study the case when the gravitino mainly decays into a neutrino and a sneutrino to obtain the most conservative constraint on the reheating temperature. When the gravitino decays into a neutrino and a sneutrino, the emitted high energy neutrinos scatter off the background neutrinos and produce charged leptons (mainly electrons and positrons), which cause electromagnetic cascades and produce many soft photons. We obtain the spectra of the high energy neutrinos as well as the spectrum of the high energy photons by integrating a set of Boltzmann equations. Requiring these photons should not alter the abundances of the light elements (D, 3He, 4He) in the universe, we can set a stringent upper bound on the reheating temperature after inflation. We find that TR ≲ 1010–1012 GeV for m32 ∼ 100 GeV-1 TeV, which is more stringent than the constraints in previous works.