Revisiting non-Gaussianity in non-attractor inflation models in the light of the cosmological soft theorem. (arXiv:2101.10682v2 [hep-th] UPDATED)
<a href="http://arxiv.org/find/hep-th/1/au:+Suyama_T/0/1/0/all/0/1">Teruaki Suyama</a>, <a href="http://arxiv.org/find/hep-th/1/au:+Tada_Y/0/1/0/all/0/1">Yuichiro Tada</a>, <a href="http://arxiv.org/find/hep-th/1/au:+Yamaguchi_M/0/1/0/all/0/1">Masahide Yamaguchi</a>
We revisit the squeezed-limit non-Gaussianity in the single-field
non-attractor inflation models from the viewpoint of the cosmological soft
theorem. In the single-field attractor models, 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 emph{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 emph{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.
We revisit the squeezed-limit non-Gaussianity in the single-field
non-attractor inflation models from the viewpoint of the cosmological soft
theorem. In the single-field attractor models, 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 emph{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 emph{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.
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