decay to the i − th degree of freedom. The composition of the reheat plasma is therefore model-dependent before its complete thermalization. However, some general statements can be made based on symmetry arguments. ρ$_{i}$ = A i 3 π $_{2}$T $^{4}$, n$_{i}$ = A i 1 π $_{2}$T $^{4}$, H ≃ A 1 / 2 ( T 2 3 M$_{P}$ ) . (436) During the quasi-adiabatic evolution of the reheated plasma, i.e., for H$_{thr}$ < H < Γ$_{d}$, we have 101 [122] In this epoch T varies in a range T$_{min}$ ≤ T ≤ T$_{max}$ , where T$_{max}$ ≈ m$_{φ}$/ 3 is reached right after the inflaton decay. Because of complete thermalization, T sharply drops from T$_{min}$ to T$_{R}$ at H$_{thr}$ , where the conservation of energy implies that T$_{R}$ = ( A 228 . 75 ) 1 / 4 T$_{min}$, = ⇒ T$_{R}$ ≤ T$_{min}$ . (437) ˙ n$_{χ}$ + 3 Hn$_{χ}$ = ∑ i ≤ j 〈 v$_{rel}$ $^{σ$_{ij}$}$→ χ 〉 n$_{i}$n$_{j}$. (438) In this section, we wish to create weakly interacting χ particles from the scatterings of the MSSM particles during the quasi-thermal phase of the universe. Recall the Boltzmann equation governing the number density of χ particles, which is given by [96, 341]: Here n$_{i}$ and n$_{j}$ are the number densities of the i − th and j − th particles, $^{σ$_{ij}$}$→ χ is the cross- section for producing χ from scatterings of i and j , and the sum is taken over all fields which participate in χ production. Also 〈 ... 〉 denotes averaging over the distribution. Since the production of χ quanta will be Boltzmann suppressed if T < m$_{χ}$/ 3. Therefore, in order to obtain the total number of χ quanta produced from scatterings, it will be sufficient to integrate the RH side of Eq. (438) from the highest temperature down to T$_{min}$ . The relic 101 One can express A i in terms of a negative chemical potential µ$_{i}$ , where A i = exp ( µ$_{i}$/T ). Note that for a large negative chemical potential, i.e., in a dilute plasma, the Bose and Fermi distributions are reduced to the Maxwell-Boltzmann distribution and give essentially the same result. The assignment of a chemical potential merely reflects the fact that the number of particles remains constant until the number-violating reactions become efficient. It does not appear as a result of a conserved quantity (such as baryon number) which is due to some symmetry. Indeed, assuming that inflaton decay does not break such symmetries, the same chemical potential to particles and anti-particles are the same. 204 1. Particle creation in a quasi-thermal phase