content_image/309047.jpg content_image/309046.jpg
We now require this upper bound to be much larger than the lower bound in Eq. (4.203). This gives 

<img src='content_image/309047.jpg'>

We now require this lower bound to be much smaller than the upper bound in Eq. (4.76). This gives 

<img src='content_image/309046.jpg'>

For all values of n , this constraint is grossly violated. Therefore, we find that this modulated decay rate scenario cannot produce the dominant contribu- tion to the observed primordial curvature perturbation within this Thermal Inflation model as it currently stands. 

