4.4 “End of Inflation” Mechanism 81 straints that are detailed in this thesis for this Thermal Inflation model. The energy density of φ during primordial inflation is with the second line coming from Eq. (4.77) regarding the dynamics of ther- mal inflation. Therefore, with the energy density of the Universe being ∼ M 2 $_{P}$H 2 ∗ , we require Substituting φ$_{BD}$ , Eq. (4.128), into Eq. (4.147) gives and substituting φ$_{BD}$ into Eq. (4.148) gives just and $^{φ}$∗ Case B ρ$_{φ,}$$_{inf}$ = ( − 1 2 m 2 $_{0}$+ h 2 ψ 2 α ∗ M 2 α − 2 P ) φ 2 $_{BD}$+ λ φ 2 n +4 BD M 2 n P (4.145) ∼ − 1 2 m 2 $_{0}$φ 2 $_{BD}$+ λ φ 2 n +4 BD M 2 n P (4.146) m$_{0}$ φ$_{BD}$ ≪ M$_{P}$$^{H}$∗ (4.147) √$_{λ φ}$ n +2 BD ≪ M n +1 P $^{H}$∗ (4.148) m$_{0}$ ≪ ( √$_{λ M}$ 2 $_{P}$H n ∗ ) 1 n +2 (4.149) $^{H}$∗ ≪ M$_{P}$ (4.150)