TY - JOUR

T1 - On soft limits of large-scale structure correlation functions

AU - Ben-Dayan, Ido

AU - Konstandin, Thomas

AU - Porto, Rafael A.

AU - Sagunski, Laura

N1 - Publisher Copyright:
© 2015 IOP Publishing Ltd and Sissa Medialab srl .

PY - 2015/2/23

Y1 - 2015/2/23

N2 - 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' are only fulfilled at the linear level, and fail at next-to-leading order for an Einstein de-Sitter universe. While applied to the velocities both proposals break down beyond leading order, we find that the '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.

AB - 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' are only fulfilled at the linear level, and fail at next-to-leading order for an Einstein de-Sitter universe. While applied to the velocities both proposals break down beyond leading order, we find that the '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.

KW - cosmological perturbation theory

KW - power spectrum

UR - http://www.scopus.com/inward/record.url?scp=84923645052&partnerID=8YFLogxK

U2 - 10.1088/1475-7516/2015/02/026

DO - 10.1088/1475-7516/2015/02/026

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AN - SCOPUS:84923645052

SN - 1475-7516

VL - 2015

JO - Journal of Cosmology and Astroparticle Physics

JF - Journal of Cosmology and Astroparticle Physics

IS - 2

M1 - 026

ER -