12 VI. CONSEQUENCES OF REHEATING/PREHEATING 2. Dark matter: A. Non-thermal Particle Creation 1. Baryogenesis and Leptogenesis: 3. Moduli and Gravitino Production Reheating and preheating lead to non-thermal particle production, as we have seen in previous sections. In cos- mology it is usually assumed that all particles start out in thermal equilibrium at the beginning of the Standard Cosmology phase. However, reheating begins with out- of-equilibrium decay of the inflaton oscillations and, as we discussed, decay products may not reach full thermal equilibrium immediately. During the transition from in- flation to the Standard Cosmology various non-thermal processes take place and the assumption of thermal equi- librium of all particles clearly breaks down. In the follow- ing, we briefly mention a few applications of non-thermal particle production. The first application is to baryo- and leptogenesis. One of the several possible mechanisms to explain the ob- served asymmetry between baryons and antibaryons is to make use of out-of-equilibrium decay of superheavy Higgs and gauge particles [74]. If reheating were purely perturbative, particles as heavy as the inflaton could be created either in inflaton decay [75] or from scatterings of inflaton decay products [49, 76]. Preheating, however, provides a mechanism to produce a large population of superheavy scalar particles much heavier than the inflaton. In [77] this was studied mak- ing use of the same chaotic inflation Lagrangian which we have used in Section 3, with the χ scalars being the superheavy Higgs or gauge fields. A full numerical study [78] showed, however, that large self-interactions may ter- minate the resonance before it becomes effective. Another way to generate to observed baryon to entropy ratio is via leptogenesis [79], a scenario in which initially an asymmetry in the lepton number is produced that is then partially converted into baryon asymmetry via SM sphalerons [80]. Preheating after inflation is a way to generate the initial lepton asymmetry. For example [81], preheating can produce a large number density of super- massive RH neutrinos in a model in which the inflaton couples to these neutrinos ψ via the standard fermionic preheating interaction term If hybrid inflation occurs at a scale close to the elec- troweak scale, then the non-thermal production of par- ticles may provide the out-of-equilibrium condition that is necessary in order to achieve electroweak baryogenesis [82]. Another application of non-thermal particle creation during reheating is to excite dark matter. It is usu- ally assumed that the dark matter particles are ther- mally distributed. This assumption is implicit in most current analyses of the prospects for dark matter detec- tion in direct and indirect experiments. However, if the dark matter particles couple to the inflaton, then non- thermal production of dark matter during reheating is to be expected. If the dark matter particles have suf- ficiently strong interactions which allows them to ther- malize during reheating, then the signatures of the initial non-thermal distribution will be washed out. However, if the interactions do not permit thermalization after in- flation, then the predictions concerning the dark matter distribution will be quite different. The production of out-of-equilibrium dark matter dur- ing preheating was put forwards in [81] and then stud- ied in detail in [76]. In the latter reference, the super- heavy dark matter particles produced during reheating were called “Wimpzillas”. Masses of Wimpzillas com- parable to the grand unified theory (GUT) scale were considered (see also [83] for a discussion of a purely grav- itational production mechanism for Wimpzillas). The dark matter abundance which can be obtained by the preheating channel is very model-dependent, whereas direct gravitational particle production produces dark matter of the required abundance for particle masses of M$_{X}$ ∼ g 1 / $^{2}$1015 GeV [83]. Preheating could also produce dangerous and un- wanted particles [84]. An example are particles with gravitationally suppressed couplings and weak scale masses that arise in many theories beyond the SM. Over- production of these particles could overclose the universe, if they are stable, or ruin the success of Big Bang nucle- osynthesis (BBN) in the case of unstable relics. Here we consider moduli and gravitino production during pre- heating. The existence of bosonic and fermionic moduli fields is common in SUSY and superstring theories. Moduli (bosonic modulus, χ , and fermionic modulus, ψ ) are typ- ically coupled to the inflaton via non-renormalizable in- teraction terms such as The production of moduli fields in chaotic and hybrid inflation reheating was analyzed in [85]. It was shown that moduli field can be parametrically amplified (their amplitude remains smaller than that of the inflaton fluc- tuations). Another important example is the gravitino, the spin L ∼ φ 4 χ m$_{pl}$ (bosonic) , L ∼ φ 2 m$_{pl}$ ¯ ψψ (fermionic) . (66) L I = gφ ¯ ψψ . (65)