content_image/316724.jpg content_image/316725.jpg content_image/316726.jpg content_image/316727.jpg content_image/316728.jpg
Rearranging this for m$_{0}$ gives 

## Case C 

<img src='content_image/316724.jpg'>

If φ is light during primordial inflation, i.e. | m$_{φ,}$$_{inf}$ | ≪ $^{H}$∗ , our potential, Eq. (4.2), can receive an appreciable SUGRA correction during primordial inflation of [52–54] 

<img src='content_image/316725.jpg'>

where $^{c}$∗ is a coupling constant. The SUGRA correction is appreciable only from the time of primordial inflation up until primordial inflation reheating, as it is suppressed at all times after this [54]. As the scale factor a grows (almost) exponentially during inflation, φ is driven rapidly to 0 , i.e. we have $^{φ}$∗ = 0 . Therefore the effective mass of φ during primordial inflation is 

In order to keep this light we therefore need 

and 

<img src='content_image/316726.jpg'>

<img src='content_image/316727.jpg'>

<img src='content_image/316728.jpg'>

