content_image/306887.jpg content_image/306888.jpg content_image/306889.jpg content_image/306890.jpg content_image/306891.jpg
straints that are detailed in this thesis for this Thermal Inflation model. 

## $^{φ}$∗ Case B 

The energy density of φ during primordial inflation is 

<img src='content_image/306887.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 

Substituting φ$_{BD}$ , Eq. (4.128), into Eq. (4.147) gives 

and substituting φ$_{BD}$ into Eq. (4.148) gives just 

<img src='content_image/306888.jpg'>

<img src='content_image/306889.jpg'>

<img src='content_image/306890.jpg'>

<img src='content_image/306891.jpg'>

