content_image/319480.jpg content_image/319481.jpg content_image/319482.jpg content_image/319483.jpg content_image/319484.jpg
Therefore, from Eq. (4.151) we require 

<img src='content_image/319480.jpg'>

To calculate φ$_{1}$ and φ$_{2}$ , the value of φ at times t$_{1}$ and t$_{2}$ respectively, we use the fact that the process is so rapid that it takes place in less than a Hubble time, so that the Universe expansion can be ignored. Then the equation of motion is 

<img src='content_image/319481.jpg'>

At the end of thermal inflation, φ is not centered on the origin, but has started to roll down the potential slightly. At this time, g $^{2}$T 2 is much smaller than m 2 $_{0}$. Therefore we have 

So we have the equation of motion 

The solution is 

<img src='content_image/319482.jpg'>

<img src='content_image/319483.jpg'>

<img src='content_image/319484.jpg'>

