content_image/305574.jpg content_image/305575.jpg content_image/305576.jpg content_image/305577.jpg content_image/305578.jpg content_image/305579.jpg
scenario for the trajectory. It is not a requirement on the model itself. In or- der that the ψ field does not affect the inflationary trajectory during thermal inflation, we require from our m mass definition, Eq. (4.3), 

Therefore we have 

From our potential, Eq. (4.2), Eq. (4.77) gives 

For Γ$_{ϕ}$ ≳ H$_{TI}$ , substituting T$_{1}$ from Eq. (4.11) into Eq. (4.79) gives 

<img src='content_image/305574.jpg'>

<img src='content_image/305575.jpg'>

<img src='content_image/305576.jpg'>

<img src='content_image/305577.jpg'>

and for Γ$_{ϕ}$ ≪ H$_{TI}$ , substituting T$_{1}$ from Eq. (4.12) into Eq. (4.79) gives 

## 4.4.3.3 Lack of Observation of φ Particles 

<img src='content_image/305578.jpg'>

Given that we have not observed any φ particles, the most liberal constraint on the present value of the effective mass of φ is 

<img src='content_image/305579.jpg'>

