In-in and δN calculations of the bispectrum fromnon-attractor single-field inflation

Abstract

In non-attractor single-field inflation models producing a scale-invariant power spectrum, the curvature perturbation on super-horizon scales grows as ℛ∝a3. This is so far the only known class of self-consistent single-field models with a Bunch-Davies initial state that can produce a large squeezed-limit bispectrum violating Maldacena's consistency relation. Given the importance of this result, we calculate the bispectrum with three different methods: using quantum field theory calculations in two different gauges, and classical calculations (the δN formalism). All the results agree, giving the local-form bispectrum parameter of flocalNL = 5(1+cs2)/(4cs2). This result is valid for arbitrary values of the speed of sound parameter, cs, for a particular non-attractor model we consider in this paper.