Monomial slow-roll e-fold count

For

V (ϕ) = λ ϕ^{n} / n

under the stated Cambridge Tripos normalization,

N_{e} = \frac{4 π G}{c ^{4} n} (ϕ_{i}^{2} - ϕ_{f}^{2}) .

If slow roll ends by kinetic-potential equality, then

ϕ_{f}^{2} ≃ \frac{n ^{2} c ^{4}}{48 π G}, N_{e} ≃ \frac{n}{12} [(\frac{ϕ _{i}}{ϕ _{f}})^{2} - 1] .

 Ancestors (7)