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Combining the frozen value $^{ψ}$∗ , Eq. (4.92), with $^{ψ}$∗ ≫ $^{δψ}$∗ and δψ 2 α − 1 ∗ ∼ H 2 α − 1 ∗ gives 

## 4.4.3.6 Thermal Fluctuation of φ 

The effective mass of φ at the end of primordial inflation is 

We have gT$_{end,inf}$ ≫ m$_{0}$ , which therefore gives 

<img src='content_image/320098.jpg'>

<img src='content_image/320096.jpg'>

<img src='content_image/320097.jpg'>

The proof is as follows. Instead of considering the time of the end of primor- dial inflation, we consider the time at the start of thermal inflation, which is of course a time at a lower temperature. For the case Γ$_{ϕ}$ ≳ H$_{TI}$ , we would be saying that 

Substituting V$_{0}$ , Eq. (4.8), into Eq. (4.101) gives 

<img src='content_image/320101.jpg'>

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<img src='content_image/320100.jpg'>

