# Consistency relations for large-scale structures: Applications for the integrated Sachs-Wolfe effect and the kinematic Sunyaev-Zeldovich effect

## TL;DR

This paper derives exact consistency relations for large-scale structure cross-correlations involving the ISW and kSZ effects, enabling tests of fundamental physics and structure modeling through observable bispectra.

## Contribution

It applies consistency relations to observational probes like ISW and kSZ effects, expressing bispectra in terms of power spectra for the first time.

## Key findings

- Cross-correlations with ISW show specific angular dependence.
- Relations depend only on the equivalence principle and Gaussian initial conditions.
- Results enable tests of fundamental physics and structure modeling.

## Abstract

Consistency relations of large-scale structures provide exact nonperturbative results for cross-correlations of cosmic fields in the squeezed limit. They only depend on the equivalence principle and the assumption of Gaussian initial conditions, and remain nonzero at equal times for cross-correlations of density fields with velocity or momentum fields, or with the time derivative of density fields. We show how to apply these relations to observational probes that involve the integrated Sachs-Wolfe effect or the kinematic Sunyaev-Zeldovich effect. In the squeezed limit, this allows us to express the three-point cross-correlations, or bispectra, of two galaxy or matter density fields, or weak lensing convergence fields, with the secondary Cosmic Microwave Background (CMB) distortion in terms of products of a linear and a nonlinear power spectrum. In particular, we find that cross-correlations with the integrated Sachs-Wolfe effect show a specific angular dependence. These results could be used to test the equivalence principle and the primordial Gaussianity, or to check the modeling of large-scale structures.