Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 310 / 4 / d / Solution

For $V=\lambda {\varphi }^4$,Thus $n_s-1=-6{ϵ}_V+2{\eta }_V=-3{ϵ}_V$. Combining this with the tensor-to-scalar ratio $r=16{ϵ}_V$ gives the quartic-inflation tilt-tensor relationThe measured tilt $n_s-1=-0.04$ would require $r\simeq 0.213$, whereas $r=0.001$ predicts $n_s-1\simeq -1.88\times 10^{-4}$. Therefore quartic slow-roll inflation is inconsistent with the stated measurements.