Probing redshift-space distortions with phase correlations

TL;DR

This paper demonstrates that the line correlation function's multipoles in redshift space effectively capture nonlinear growth and velocity effects, providing complementary information to traditional statistics for testing gravity.

Contribution

It introduces the multipole expansion of the redshift-space line correlation function, highlighting its sensitivity to nonlinear structure growth and its potential to distinguish gravity models.

Findings

Monopole, quadrupole, and hexadecapole encode most information.

Line correlation multipoles are sensitive to nonlinear density and velocity coupling.

Combined with other statistics, they can help test modified gravity theories.

Abstract

Redshift-space distortions are a sensitive probe of the growth of large-scale structure. In the linear regime, redshift-space distortions are fully described by the multipoles of the two-point correlation function. In the nonlinear regime, however, higher-order statistics are needed to capture the full information of the galaxy density field. In this paper, we show that the redshift-space line correlation function--which is a measure of Fourier phase correlations--is sensitive to the nonlinear growth of the density and velocity fields and to the nonlinear mapping between real and redshift space. We expand the line correlation function in multipoles, and we show that almost all of the information is encoded in the monopole, quadrupole, and hexadecapole. We argue that these multipoles are highly complementary to the multipoles of the two-point correlation function: first, because they are directly sensitive to the difference between the density and the velocity coupling kernels, which is a purely nonlinear quantity; and second, because the multipoles are proportional to different combinations of $f$ and $\sigma_8$. Measured in conjunction with the two-point correlation function and the bispectrum, the multipoles of the line correlation function could therefore allow us to disentangle efficiently these two quantities and to test modified theories of gravity.