AI 中文总结
该研究通过二阶微扰理论证明，曲率（kurvature）并非与R直接相关，其大尺度白噪声源于外曲率，不会在宇宙学曲率扰动R中留下红外遗迹，解决了曲率的红外发散问题。
AI 中文摘要
曲率（kurvature）是近期发现的曲率不变量，有观点认为即使物质非线性很小，它也会因硬-硬动量耦合获得超视界（即大尺度）白噪声；若曲率通过泊松方程直接与宇宙学曲率扰动R相关，该白噪声会导致红外发散的方差，对紫外硬模物理敏感。但这种关系通常不成立：曲率并非固有3曲率，在共动切片上包含外曲率项，且线性阶以上固有曲率不通过泊松方程与R关联。我们在辐射主导时期（与CMB可观测量相关）用二阶微扰理论验证该推论：二次硬-硬复合项确实会在曲率密度中产生大尺度白噪声，但哈密顿约束将其分离为固有曲率和外剪切（或等价为密度和膨胀），仅外项携带视界上类似普通密度涨落的增长无量纲曲率密度；直接硬-硬曲率功率是紫外收敛的，评估时由视界尺度模式主导，不会从纯紫外模式在R中留下红外遗迹；相比之下，从曲率构造曲率势的泊松结构是红外发散且对截断敏感的，其白噪声源于辐射流体中非线声波拍模相关的外曲率。
英文摘要
Kurvature, a recently identified curvature invariant, has been argued to acquire superhorizon, or large-scale, white noise from hard-hard momentum coupling even when matter nonlinearities are small. If kurvature were related directly to cosmological curvature perturbations R through a Poisson equation, this white noise would cause an infrared-divergent variance sensitive to ultraviolet hard-mode physics. However, this relation does not generically hold. Kurvature is not intrinsic 3-curvature: on comoving slices it contains extrinsic-curvature terms, and intrinsic curvature is not related to R by a Poisson equation beyond linear order. We test this inference with second-order perturbation theory in radiation domination, relevant to CMB observables. Quadratic hard-hard composites do generate large-scale white noise in the kurvature density, but the Hamiltonian constraint separates it into intrinsic curvature and extrinsic shear, or equivalently density and expansion. Only the extrinsic terms carry the growing dimensionless kurvature density that mimics an ordinary density fluctuation above the horizon. The direct hard-hard curvature power is ultraviolet convergent, dominated by horizon-scale modes at evaluation, and leaves no IR relic in R from purely ultraviolet modes. By contrast, the Poisson construction of a curvature potential from kurvature is infrared divergent and cutoff sensitive; its white noise arises from extrinsic curvature associated with nonlinear acoustic beat modes in a radiation fluid.
Comments20 pages, 4 figures
