Equal-time Consistency Relations in the Large-Scale Structure of the Universe

TL;DR

The authors derive an equal-time consistency relation for the soft limit of (n+1)-point dark matter correlators by incorporating a non-uniform gravitational force through two spatial gradients. The resulting squeezed-limit expression for the dark matter bispectrum relates the long-wavelength mode to the short-scale power via a $P_L(q)$ factor and derivatives with respect to $k$ and the growth factor $D(a)$. They generalize this to higher-order correlators and discuss its applicability to dark matter but not galaxies due to time-growth mapping. The halo model is then shown to satisfy the relation up to scales around $1\,h\,\mathrm{Mpc}^{-1}$, with the squeezed bispectrum effectively factorizing into $P_L(q)$ times a nonlinear halo contribution, providing a nontrivial consistency check for analytical models of large-scale structure.

Abstract

We discuss the consistency relations involving the soft limit of the (n + 1)-correlator functions of dark matter at equal times and their consequences for the halo model.

Figures (1)

• Figure 1: The function $\langle b_1\rangle(k_1)$ as a function of $k_1$.