Typically this time scale can be, t$_{th}$ ∼ c 7 / 4 r 10 21 for m$_{φ}$ ∼ 10 13 GeV and ρ$_{inf}$ ∼ 10 64 (GeV) $^{4}$, comparable to the perturbative inflaton decay rate, see Eq. (376). One of the most interesting effects of preheating is the copious production of particles which have a mass greater than the inflaton mass m$_{φ}$ . Such processes are impossible in perturbation theory and in the theory of narrow parametric resonance. However, superheavy χ -particles with mass M ≫ m$_{φ}$ can be produced in the regime of a broad parametric resonance. For very small φ ( t ) the change in the frequency of oscillations ω ( t ) ceases to be adiabatic when the adiabaticity condition is violated [100] The momentum dependent frequency, ω$_{k}$ ( t ) violates the above condition when The maximal range of momenta for which particle production occurs corresponds to φ ( t ) = $^{φ}$∗ , where $^{φ}$∗ ≈ 1 2 √ m$_{φ}$ ˆ φ h . The maximal value of momentum for particles produced at that epoch can be estimated by k 2 max + m 2 χ = hm$_{φ}$ ˆ φ 2 . The resonance becomes efficient for hm$_{φ}$ ˆ φ > ∼ 4 m 2 $_{χ}$. Thus, the inflaton oscillations may lead to a copious production of superheavy particles with m$_{χ}$ ≫ m if the amplitude of the field φ is large enough, h ˆ φ > ∼ 4 m 2 $_{χ}$/m$_{φ}$ . During the second stage of preheating both m$_{φ}$ and ˆ φ change very rapidly, but their product remains almost constant because the energy density of the field φ , which is propor- tional to m 2 $_{φ}$ˆ φ $^{2}$/ 2, practically does not change until the very end of preheating. Therefore it is sufficient to check that hm ˆ φ > ∼ 4 m 2 χ at the end of the first stage of preheating. One can represent this criterion in a simple form [100]: For example, one may take m$_{χ}$ = 2 m$_{φ}$ and h ≈ 0 . 007, which corresponds to q$_{0}$ = h 2 ˆ φ $^{2}$/m2 φ = 10 6 . The production of χ -particles with m$_{χ}$ = 10 m$_{φ}$ is possible for h > ∼ 10 − $^{2}$. Anyway, as we shall see in a realistic SUSY case, the existence of heavy mass of χ induced by the flat direction VEV of MSSM can kinematically block resonant preheating altogether [123], see Sec. VI D 1. m$_{χ}$ < ∼ m$_{φ}$ √$_{2}$ q 1 / 4 ≈ m$_{φ}$ ( hM$_{p}$ 3 m$_{φ}$ $_{ln}$− 1 10 $^{12}$m$_{φ}$ h $^{5}$M$_{p}$ ) 1 / 2 . (385) dω ( t ) dt ≥ ω $^{2}$( t ) . (383) k 2 + m 2 χ < ∼ ( h $^{2}$φm$_{φ}$ ˆ φ ) 2 / 3 − h 2 ˆ φ 2 . (384) 180