4.5 Modulated Decay Rate 104 Then, from our mass definition m , Eq. (4.3), we obtain Regarding the constraints that appear in Section 4.4.3, all are relevant to this modulated decay scenario except for those that appear in Section 4.4.3.10, as we do not require that the transition from thermal inflation to thermal waterfall field oscillation be sufficiently fast here, as well as those appearing in Section 4.4.3.11, as the spectator field will not be oscillating in this scenario (see Section 4.5.2.2). After the end of thermal inflation, we require there to exist an amount of time, i.e. an amount of Universe expansion, prior to the decay of the φ field. This is so that the modulated decay rate mechanism can have an effect. If the φ field decayed immediately after the end of thermal inflation, the decay rate would not be effectively modulated. Therefore, we require Substituting Eqs. (4.10) and (4.195) into here gives H$_{T I}$ > Γ (4.202) m$_{0}$ > √$_{λ g}$ 2 n $^{+2}$M$_{P}$ (4.203) f$_{NL}$ ∼ − 5 [ 1 + 2 α − 1 α ( m 2 $_{0}$M 2 α − 2 P 2 h $^{2}$ψ2 α ∗ − 1 )] (4.201) 4.5.2 Constraining the Free Parameters 4.5.2.1 Time for φ Decay