On the non-linear scale of cosmological perturbation theory

Abstract

We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

38 pages, 11 figures; v2 minor changes, references added. Matches published version

References in corpus (10)

• The Effective Field Theory of Cosmological Large Scale Structures
• Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space
• On the Robustness of the Acoustic Scale in the Low-Redshift Clustering of Matter
• Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations
• Symmetries and Consistency Relations in the Large Scale Structure of the Universe
• Multi-Point Propagators in Cosmological Gravitational Instability
• Galilean invariance and the consistency relation for the nonlinear squeezed bispectrum of large scale structure
• Large-N expansions applied to gravitational clustering
• Using the Zeldovich dynamics to test expansion schemes
• Relation between standard perturbation theory and regularized multi-point propagator method

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