content_image/304738.jpg content_image/304739.jpg content_image/304741.jpg content_image/304742.jpg
while for all other n and α values, the above inequality is reversed, giving 

<img src='content_image/304738.jpg'>

<img src='content_image/304739.jpg'>

## 4.4.3.7 Thermalization of φ 

In order that φ interacts with the thermal bath and therefore that we actually have the g $^{2}$T $^{2}$φ2 term in our potential, Eq. (4.2), we require 

where Γ$_{therm}$ is the thermalization rate of φ , which is given by 

<img src='content_image/304741.jpg'>

<img src='content_image/304742.jpg'>

where n ∼ T 3 is the number density of particles in the thermal bath, σ is the scattering cross-section for the interaction of φ and the particles in the 

