Revisiting non-Gaussianity in non-attractor inflation models in the light of the cosmological soft theorem

We revisit squeezed-limit non-Gaussianity in single-field non-attractor inflation models from the viewpoint of the cosmological soft theorem. In single-field attractor models, an inflaton's trajectories with different initial conditions effectively converge into a single trajectory in the phase space, and hence there is only one clock degree of freedom (DoF) in the scalar part. Its long-wavelength perturbations can be absorbed into the local coordinate renormalization and lead to the so-called consistency relation between n- and (n+1)-point functions. On the other hand, if the inflaton dynamics deviates from the attractor behavior, its long-wavelength perturbations cannot necessarily be absorbed and the consistency relation is expected not to hold any longer. In this work, we derive a formula for the squeezed bispectrum including the explicit correction to the consistency relation, as a proof of its violation in the non-attractor cases. First one must recall that non-attractor inflation needs to be followed by attractor inflation in a realistic case. Then, even if a specific non-attractor phase is effectively governed by a single DoF of phase space (represented by the exact ultra-slow-roll limit) and followed by a single-DoF attractor phase, its transition phase necessarily involves two DoF in dynamics and hence its long-wavelength perturbations cannot be absorbed into the local coordinate renormalization. Thus, it can affect local physics, even taking account of the so-called local observer effect, as shown by the fact that the bispectrum in the squeezed limit can go beyond the consistency relation. More concretely, the observed squeezed bispectrum does not vanish in general for long-wavelength perturbations exiting the horizon during a non-attractor phase.

Automated summary

This study explores the squeezed-limit non-Gaussianity in single-field non-attractor inflation models, showing that long-wavelength perturbations can affect the consistency relation. Non-attractor inflation needs to be followed by attractor inflation in a realistic case, with a transition phase involving two degrees of freedom in dynamics.