## B. Non-perturbative inflaton scatterings 

Many studies have been devoted to understand non-perturbative effects during reheating. Various non-thermal and non-perturbative effects may lead to a rapid transfer of the inflaton energy to other degrees of freedom by the process known as preheating . The requirement is that the inflaton quanta couple to other (essentially massless) field χ through, i.e. terms like φ $^{2}$χ$^{2}$. The quantum modes of χ may then be excited during the inflaton oscillations via a parametric resonance . Preheating has been treated both analytically [97–100, 112– 119, 124, 541, 762–771] (for an elaborate discussion on reheating and preheating, see [100]), and numerically on lattice simulations [101–111, 772]. Like bosons, fermions can also be excited during preheating [95, 338, 773–776]. In fact, it has been argued that fermionic preheating is more efficient than bosonic preheating, however these fermions can not be related to the chiral fermions of the SM. The SM fermions can only couple to a gauge singlet inflaton via non-renormalizable dimensional 5 operators, therefore the effective couplings are very small. During preheating it is possible to excite gravity waves [727, 777–786], magnetic field [787, 788], gravitino abundance with spin ± 1 / 2 , ± 3 / 2 [658, 789–794], moduli and non-thermal stringy relics [795], phase transitions [725, 796]. A successful cold electroweak baryogenesis were also studied in the context of preheating [797–799]. For a recent review on reheating and preheating, see [125]. 

During preheating, it is also possible to excite the perturbed FRW metric potential, see [215, 781, 800–803], however as shown in Ref. [804], it is hard to excite large metric perturbations in g $^{2}$φ$^{2}$χ2 theory. For large g and large inflaton VEV, φ , the initial χ pertur- bations in the vacuum are very much suppressed, see also [805]. The second order metric perturbations can also leave non-Gaussian signature during preheating [243–246, 579], which may put severe constraint on a simple λφ 4 inflation model [243]. 

## 1. Parametric Resonance 

Let us briefly review the initial stages of a gauge singlet inflaton decay, which happens typically non-perturbatively, i.e. preheating, in most of the non-SUSY cases. In SUSY, there are complications with the potential itself, as well as the presence of MSSM flat directions. 

