Speaker
Laura Sagunski
(DESY, Germany)
Description
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.
