Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 1 / 15B / d / Solution

For the quartic potential,Integrating the result of part (c) along the trajectory from ${\varphi }_i$ to ${\varphi }_f$ givesBecause the negative field rolls toward zero, ${\varphi }_i<{\varphi }_f<0$ and $|{\varphi }_i|>|{\varphi }_f|$, so this monomial slow-roll e-fold count is positive.