Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 310 / 4 / d / Solution

The expressions in part c implySince the tensor-to-scalar ratio is $r=16ϵ$,For positive $\alpha$, this class predicts a red scalar tilt andA blue tilt with positive $r$, or $r\ge 8(1-n_s)$, is incompatible. An allowed pair fixes $\alpha =2r/[8(1-n_s)-r]$, subject to slow roll and observational bounds.