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 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.

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根据宇宙软定理重新审视非吸引子暴胀模型中的非高斯性

我们从宇宙软定理的角度重新审视了单场非吸引子暴胀模型中的挤压极限非高斯性。在单场吸引子模型中，不同初始条件的暴胀子轨迹在相空间中有效地收敛到一个单一的轨迹中，因此标量部分只有一个时钟自由度（DoF）。它的长波长扰动可以被​​吸收到局部坐标重整化中，并导致n点函数和(n+1)点函数之间的所谓一致性关系。另一方面，如果暴胀子动力学偏离吸引子行为，它的长波长扰动不一定被吸收，并且预计一致性关系不再成立。在这项工作中，我们推导出压缩双谱的公式，包括对一致性关系的显式校正，作为在非吸引子情况下违反其的证明。首先必须记住，在现实情况下，非吸引子膨胀需要跟随吸引子膨胀。然后，即使一个特定的非吸引子阶段有效地由相空间的单个自由度（由精确的超慢滚极限表示）控制，并且随后是单个自由度吸引子阶段，它的过渡阶段也必然涉及两个自由度动力学及其长波长扰动不能被吸收到局部坐标重整化中。因此，它可以影响局部物理，即使考虑到所谓的局部观察者效应，正如压缩极限中的双谱可以超越一致性关系的事实所示。