有效场论中膨胀软模式的局部性
Locality in effective field theory for inflationary soft modes
AI总结：
本文研究了膨胀软模式的有效场论中局部性条件，提出了一种量子态的局部性要求，该要求确保每个局部宇宙中的硬模式态仅通过同一区域内的软模式值依赖于软模式。当该条件满足时，粗粒化后的软模式动力学保持局部性，硬模式对超视界曲率扰动相关函数的环修正被扰动抑制。这为判断因硬模式增强修正而破坏梯度展开的情况提供了模型无关的诊断。此外，该局部性条件还推导出广义软定理，从而在额外假设下得到标准一致性关系。本文还表明，局部性条件保证了在大规范变换下不变的算子相关函数的红外发散不存在。因此，硬模式态的局部性为膨胀软模式的有效描述、广义软定理、硬模式环修正的抑制以及可观察相关函数的红外正则性提供了一个统一的标准。
摘要：
梯度展开和单独宇宙方法为在粗粒化掉短波长自由度后提供了膨胀软模式的有效描述。我们对量子态提出局部性条件，要求每个局部宇宙中的硬模式态仅通过同一区域内的软模式值依赖于软模式。当该条件满足时，粗粒化后的软模式动力学保持局部性，并且硬模式对超视界曲率扰动相关函数的环修正被扰动抑制。这为判断因硬模式增强修正而破坏梯度展开的情况提供了模型无关的诊断。我们进一步表明，相同的局部性条件推导出广义软定理，从而在额外假设下得到标准一致性关系。本文还表明，局部性条件保证了在大规范变换下不变的算子相关函数的红外发散不存在。因此，硬模式态的局部性为膨胀软模式的有效描述、广义软定理、硬模式环修正的抑制以及可观察相关函数的红外正则性提供了一个统一的标准。
英文摘要：
The gradient expansion and the separate universe approach provide an effective description of inflationary soft modes after coarse-graining shorter-wavelength degrees of freedom. We formulate a locality condition on the quantum state, requiring that the hard-mode state in each local universe depend on the soft modes only through the local soft-mode values in the same patch. When this condition is satisfied, the coarse-grained soft-mode dynamics remains local, and loop corrections from hard modes to superhorizon correlators of the adiabatic curvature perturbation are perturbatively suppressed. This provides a model-independent diagnosis of when enhanced corrections due to hard modes can invalidate the gradient expansion. We further show that the same locality condition implies a generalized soft theorem, from which the standard consistency relations follow under additional assumptions. This formulation clarifies the origin of possible deviations from the standard consistency relations in multi-field systems or in a non-attractor background. We also show that the locality condition guarantees the absence of infrared divergences for the correlators of operators invariant under a large gauge transformation. Thus, locality of the hard-mode state provides a unified criterion for the effective description of inflationary soft modes, generalized soft theorems, the suppression of hard-mode loop corrections, and the infrared regularity of observable correlators.
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