White noise in the second-order kurvature density is real, but it is not inherited by the comoving curvature perturbation as an infrared pole, invalidating the k_BH bound on the small-scale primordial power spectrum.
Lettingx µ(τ) be a fluid element’s worldline, withτthe proper time comoving with the fluid, one has uµ = dxµ dτ
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The Fate of Large Scale White Noise in Second-Order Cosmological Perturbation Theory
White noise in the second-order kurvature density is real, but it is not inherited by the comoving curvature perturbation as an infrared pole, invalidating the k_BH bound on the small-scale primordial power spectrum.