In-in and δ<i>N</i>calculations of the bispectrum from non-attractor single-field inflation

Abstract

In non-attractor single-field inflation models producing a scale-invariant\npower spectrum, the curvature perturbation on super-horizon scales grows as\n${\\cal R}\\propto a^3$. This is so far the only known class of self-consistent\nsingle-field models with a Bunch-Davies initial state that can produce a large\nsqueezed-limit bispectrum violating Maldacena's consistency relation. Given the\nimportance of this result, we calculate the bispectrum with three different\nmethods: using quantum field theory calculations in two different gauges, and\nclassical calculations (the $\\delta N$ formalism). All the results agree,\ngiving the local-form bispectrum parameter of\n$f^{local}_{NL}=5(1+c_s^2)/(4c_s^2)$. This result is valid for arbitrary values\nof the speed of sound parameter, $c_s$, for a particular non-attractor model we\nconsider in this paper.\n