Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 70 / 1 / c / Solution

At leading order the scalar curvature power and total tensor power areApplying the preceding $d/d\ln k$ relation gives the scalar spectral index $n-1=-6{ϵ}_V+2{\eta }_V$ and the tensor spectral index $n_T=-2{ϵ}_V$. For this hilltop,Thus, fifty e-folds before the end,The tiny $-6{ϵ}_V$ contribution and finite-endpoint corrections have been omitted in the quoted leading scalar tilt. The tensor tilt is nearly zero but slightly negative; treating $H$ as exactly constant in its spectrum would incorrectly discard its leading nonzero value.