Potential slow-roll parameter

The potential slow-roll parameter isUnder the slow-roll equations, ${\dot{\varphi }}^2/(2V)\simeq {ϵ}_V/3$.

At horizon exit during single-field slow-roll inflation, $d/d\log k\simeq -M_{\mathrm{Pl}}^2(V^{\prime }/V)d/d\Phi$. Applying this operator to the potential slow-roll parameter and the second potential slow-roll parameter yields the displayed leading-order flow equations. Corrections to the horizon-exit derivative contribute only at higher slow-roll order here.

Despite its notation, ${\xi }_V^2$ need not be nonnegative. It is the signed dimensionless derivative combination entering the leading running of the scalar spectral index.

The second potential slow-roll parameter isSlow roll usually requires both ${ϵ}_V\ll 1$ and $|{\eta }_V|\ll 1$.