content_image/306525.jpg content_image/306526.jpg content_image/306524.jpg content_image/306523.jpg content_image/306522.jpg
we obtain 

## $^{φ}$∗ Case A 

The energy density of φ during primordial inflation is 

<img src='content_image/306525.jpg'>

<img src='content_image/306526.jpg'>

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 

and 

<img src='content_image/306524.jpg'>

<img src='content_image/306523.jpg'>

Substituting 〈 φ 〉 , Eq. (4.7), into Eq. (4.142) gives the same constraint as from substituting 〈 φ 〉 into Eq. (4.143). This constraint is 

<img src='content_image/306522.jpg'>

However, for all viable parameter values in our model, this constraint is never the dominant constraint when we consider it alongside all of the other con- 

