4.4 “End of Inflation” Mechanism 78 Rearranging this for m$_{0}$ gives If φ is light during primordial inflation, i.e. | m$_{φ,}$$_{inf}$ | ≪ $^{H}$∗ , our potential, Eq. (4.2), can receive an appreciable SUGRA correction during primordial inflation of [52–54] where $^{c}$∗ is a coupling constant. The SUGRA correction is appreciable only from the time of primordial inflation up until primordial inflation reheating, as it is suppressed at all times after this [54]. As the scale factor a grows (almost) exponentially during inflation, φ is driven rapidly to 0 , i.e. we have $^{φ}$∗ = 0 . Therefore the effective mass of φ during primordial inflation is In order to keep this light we therefore need and Case C m$_{0}$ ≪ 100 √ M$_{P}$   $^{H}$$^{3}$$^{α}$$^{−}$$^{2}$ ∗$_{h}$ ( √$_{λ}$ M n $_{P}$H 2 ∗ ) 2 α$_{−}$ 1 n +2    1 2 α$_{−}$ 2 (4.130) Δ V ∼ $^{c}$∗H 2 ∗ φ 2 (4.131) m 2 φ, inf ∼ − m 2 0 + $^{c}$∗H 2 ∗ (4.132) m$_{0}$ ≪ $^{H}$∗ (4.133) $^{c}$∗ < 1 (4.134)