4.3 φ Decay Rate, Spectral Index and Tensor Fraction 59 both primordial inflation reheating and thermal inflation reheating, as this value corresponds to the number of relativistic degrees of freedom in the Standard Model. We have 4.3.2.2 The Case Γ$_{ϕ}$ ≪ H TI Using a ∝ T − 8 3 for the period between the end of primordial inflation and the start of thermal inflation, as well as for the period between the end of thermal inflation and thermal inflation reheating and using a ∝ T − 1 for all other times, we have Using T$_{piv}$ =9 . 830 × 10 − 13 GeV (Eq. (4.47)), we obtain $^{N}$∗ as where we have used $^{g}$∗ ≈ 10 2 as the number of spin states (effective relativistic degrees of freedom) of all of the particles in the thermal bath at the time $^{N}$∗ ≈ ln ( (1 . 5637 × 10 38 GeV − $^{1}$) $^{H}$∗ 0 . 002 ) + 2 3 ln ( 9Γ 10 π $^{2}$H $_{∗}$) + 1 4 ln ( 10 π $^{2}$(9 . 830 × 10 − 13 GeV ) 4 9 M 2 $_{P}$Γ 2 ) − N$_{TI}$ (4.52) e N$_{∗}$ = $^{H}$∗ k ( T$_{start,TI}$ T$_{end,inf}$ ) 8 3 ( T$_{reh,TI}$ T$_{end,TI}$ ) 8 3 T$_{piv}$ T$_{reh,TI}$ e − N$_{TI}$ (4.51) H − 1 ∗ = $^{a}$∗ a$_{end,inf}$ a$_{end,inf}$ a$_{start,TI}$ a$_{start,TI}$ a$_{end,TI}$ a$_{end,TI}$ a$_{reh,TI}$ a$_{reh,TI}$ a$_{eq}$ a$_{eq}$ a$_{piv}$ H − 1 piv (4.49) = e − N$_{∗}$ a$_{end,inf}$ a$_{start,TI}$ e − $_{N$_{TI}$}$a$_{end,TI}$ a$_{reh,TI}$ a$_{reh,TI}$ a$_{eq}$ a$_{eq}$ a$_{piv}$ H − 1 piv (4.50)