The Universe after inflation: the wide resonance case

We numerically study the decay of massive and massless inflatons φ into massive excitations X, via a φ2X2 coupling, in the expanding Universe. We find that a wide enough resonance can withstand expansion of the Universe, and we determine the range of parameters in which that happens. For a massive inflaton, the effective production of particles with mass ten times that of the inflaton requiresvery large values of the resonance parameter q, q ≳ 108. For these large q, the maximal size of produced fluctuations is significantly suppressed by back reaction, but at least in the Hartree approximation they are still not negligible. For a massless inflaton with a λφ44 potential, the expansion of the Universe completely prevents resonant production of particles with masses larger than λφ(0) for values of q smaller than 106.