The Universe after inflation: the wide resonance case

Abstract

We study numerically the decay of massive and massless inflatons into massive excitations, via a $φ^2 X^2$ coupling, in the expanding Universe. We find that a wide enough resonance can survive the Universe expansion, though account for the expansion is very important for determining precisely how wide it should be. For a massive inflaton, the effective production of particles with mass ten times that of the inflaton requires very large values of the resonance parameter $q$, $q\gsim 10^8$. For these large $q$, the maximal size of produced fluctuations is significantly suppressed by the back reaction, but at least within the Hartree approximation they are still not negligible. For the massless inflaton with a $λφ^4/4$ potential, the Universe expansion completely prevents a resonance production of particles with masses larger than $\sqrtλφ(0)$ for $q$ up to $q=10^6$.

Figures (3)

• Figure 1: Maximal value of the variance of fluctuations in Model 1 as a function of the resonance parameter. Dotted lines correspond to no back reaction and are fitted by a power law. Solid curves are obtained in the Hartree approximation. The dashed straight line is a power law fit to the Hartree data.
• Figure 2: Fluctuation variance in Model 1, as a function of time, for two values of the mass of the fluctuating field; back reaction of fluctuations on the inflaton field was included in the Hartree approximation.
• Figure 3: Time evolution of the homogeneous inflaton field and the fluctuation variance in Model 1 in the Hartree approximation, for given values of the parameters.