Multi-Point Propagators in Cosmological Gravitational Instability

TL;DR

This paper introduces multi-point propagators in cosmological perturbation theory, demonstrating their decay behavior, measuring them in simulations, and applying them to improve predictions of the bispectrum at small scales.

Contribution

It generalizes the large-$k$ behavior of propagators to arbitrary order and connects nonlinear power spectrum corrections to higher-order correlations.

Findings

Multi-point propagators decay at the same rate as two-point propagators.

Numerical simulations confirm the high-$k$ resummation results.

Application to the bispectrum shows improved shape dependence predictions.

Abstract

We introduce the concept of multi-point propagators between linear cosmic fields and their nonlinear counterparts in the context of cosmological perturbation theory. Such functions express how a non-linearly evolved Fourier mode depends on the full ensemble of modes in the initial density field. We identify and resum the dominant diagrams in the large-$k$ limit, showing explicitly that multi-point propagators decay into the nonlinear regime at the same rate as the two-point propagator. These analytic results generalize the large-$k$ limit behavior of the two-point propagator to arbitrary order. We measure the three-point propagator as a function of triangle shape in numerical simulations and confirm the results of our high-$k$ resummation. We show that any $n-$point spectrum can be reconstructed from multi-point propagators, which leads to a physical connection between nonlinear corrections to the power spectrum at small scales and higher-order correlations at large scales. As a first application of these results, we calculate the reduced bispectrum at one-loop in renormalized perturbation theory and show that we can predict the decrease in its dependence on triangle shape at redshift zero, when standard perturbation theory is least successful.