 Quadratic hilltop slow-roll prediction

ID: quadratic-hilltop-slow-roll-prediction

For

V (ϕ) = V_{0} - m^{2} ϕ^{2} /2

with

V_{0}

dominant,

η_{V} ≃ - \frac{m ^{2} M _{Pl}^{2}}{V _{0}}, ϵ_{V} ≃ \frac{1}{2} η_{V}^{2} \frac{ϕ ^{2}}{M _{Pl}^{2}} .

N

e-folds remain and

n_{s} - 1 ≃ 2 η_{V}

, then

ϕ = ϕ_{e} e^{(n_{s} - 1) N /2}, r ≃ 2 (n_{s} - 1)^{2} (\frac{ϕ _{e}}{M _{Pl}})^{2} e^{(n_{s} - 1) N} .

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