First test of the consistency relation for the large-scale structure using the anisotropic three-point correlation function of BOSS DR12 galaxies (An explanatory video is available at https://youtu.be/Zi36ooLPhss.)

Abstract

We present, for the first time, an observational test of the consistency relation for the large-scale structure (LSS) of the Universe through a joint analysis of the anisotropic two- and three-point correlation functions (2PCF and 3PCF) of galaxies. We parameterise the breakdown of the LSS consistency relation in the squeezed limit by $E_{\rm s}$, which represents the ratio of the coefficients of the shift terms in the second-order density and velocity fluctuations. $E_{\rm s}\neq1$ is a sufficient condition under which the LSS consistency relation is violated. A novel aspect of this work is that we constrain $E_{\rm s}$ by obtaining information about the nonlinear velocity field from the quadrupole component of the 3PCF without taking the squeezed limit. Using the galaxy catalogues in the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12, we obtain $E_{\rm s} = -0.92_{-3.26}^{+3.13}$, indicating that there is no violation of the LSS consistency relation in our analysis within the statistical errors. Our parameterisation is general enough that our constraint can be applied to a wide range of theories, such as multicomponent fluids, modified gravity theories, and their associated galaxy bias effects. Our analysis opens a new observational window to test the fundamental physics using the anisotropic higher-order correlation functions of galaxy clustering.