On the scalar consistency relation away from slow roll

Understand

As is well known, the non-Gaussianity parameter $f_{_{\rm NL}}$, which is often used to characterize the amplitude of the scalar bi-spectrum, can be expressed completely in terms of the scalar spectral index $n_{\rm s}$ in the squeezed limit, a relation that is referred to as the consistency condition.

• This relation, while it is largely discussed in the context of slow roll inflation, is actually expected to hold in any single field model of inflation, irrespective of the dynamics of the underlying model, provided inflation occurs on the attractor at late times.
• In this work, we explicitly examine the validity of the consistency relation, analytically as well as numerically, away from slow roll.
• Analytically, we first arrive at the relation in the simple case of power law inflation.