Probing redshift-space distortions with phase correlations

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 non-linear 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 non-linear growth of the density and velocity fields. 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 non-linear quantity; and second, because the multipoles are proportional to different combinations of f and σ8. 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.