On Soft Limits of Large-Scale Structure Correlation Functions

Ben-Dayan, Ido; Porto, Rafael A.; Sagunski, Laura; Konstandin, Thomas

Preprint/Internal Report

PUBDB-2014-04194

On Soft Limits of Large-Scale Structure Correlation Functions

Ben-Dayan, I. (Corresponding Author)DESY* ; Konstandin, T.DESY* ; Porto, R. A. ; Sagunski, L.DESY*

2014

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Report No.: DESY-14-215; arXiv:1411.3225

Abstract: We study soft limits of correlation functions for the density and velocity fields in the theory of structure formation. First, we re-derive the (resummed) consistency conditions at unequal times using the eikonal approximation. These are solely based on symmetry arguments and are therefore universal. Then, we explore the existence of equal-time relations in the soft limit which, on the other hand, depend on the interplay between soft and hard modes. We scrutinize two approaches in the literature: the time-flow formalism, and a background method where the soft mode is absorbed into a locally curved cosmology. The latter has been recently used to set up (angular averaged) `equal-time consistency relations. We explicitly demonstrate that the time-flow relations and equal-time consistency conditions quantitatively approximates the perturbative results for the density contrast. Thus, we generalize the background method to properly incorporate the effect of curvature in the density and velocity fluctuations on short scales, and discuss the reasons behind this discrepancy. We conclude with a few comments on practical implementations and future directions.

Keyword(s): cosmological perturbation theory (LCSH) ; power spectrum (LCSH) ; velocity: correlation function ; density: correlation function ; approximation: eikonal ; velocity: fluctuation ; density: fluctuation ; curvature: effect ; higher-order: 0 ; higher-order: 1 ; cosmological model