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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 parameterize the breakdown of the LSS consistency relation in the squeezed limit by Es, which represents the ratio of the coefficients of the shift terms in the second-order density and velocity fluctuations. Es ≠ 1 is a sufficient condition under which the LSS consistency relation is violated. A novel aspect of this work is that we constrain Es by obtaining information about the non-linear 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 parameterization 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. 

Abstract We infer the growth of large scale structure over the redshift range 0.4 ≲z≲ 1 from the cross-correlation of spectroscopically calibrated Luminous Red Galaxies (LRGs) selected from the Dark Energy Spectroscopic Instrument (DESI) legacy imaging survey with CMB lensing maps reconstructed from the latestPlanckand ACT data.We adopt a hybrid effective field theory (HEFT) model that robustly regulates the cosmological information obtainable from smaller scales, such that our cosmological constraints are reliably derived from the (predominantly) linear regime.We perform an extensive set of bandpower- and parameter-level systematics checks to ensure the robustness of our results and to characterize the uniformity of the LRG sample.We demonstrate that our results are stable to a wide range of modeling assumptions, finding excellent agreement with a linear theory analysis performed on a restricted range of scales.From a tomographic analysis of the four LRG photometric redshift bins we find that the rate of structure growth is consistent with ΛCDM with an overall amplitude that is ≃ 5-7% lower than predicted by primary CMB measurements with modest (∼ 2σ) statistical significance.From the combined analysis of all four bins and their cross-correlations withPlanckwe obtainS₈= 0.765 ± 0.023, which is less discrepant with primary CMB measurements than previous DESI LRG crossPlanckCMB lensing results.From the cross-correlation with ACT we obtainS₈= 0.790^+0.024_-0.027, while when jointly analyzingPlanckand ACT we findS₈= 0.775^+0.019_-0.022from our data alone andσ₈= 0.772^+0.020_-0.023with the addition of BAO data.These constraints are consistent with the latestPlanckprimary CMB analyses at the ≃ 1.6-2.2σlevel, and are in excellent agreement with galaxy lensing surveys. 

ABSTRACT We report a new test of modified gravity theories using the large-scale structure of the Universe. This paper is the first attempt to (1) apply a joint analysis of the anisotropic components of galaxy two- and three-point correlation functions (2 and 3PCFs) to actual galaxy data and (2) constrain the non-linear effects of degenerate higher-order scalar-tensor (DHOST) theories on cosmological scales. Applying this analysis to the Baryon Oscillation Spectroscopic Survey (BOSS) data release 12, we obtain the lower bounds of −1.655 < ξt and −0.504 < ξs at the $$95{{\ \rm per\ cent}}$$ confidence level on the parameters characterizing the time evolution of the tidal and shift terms of the second-order velocity field. These constraints are consistent with GR predictions of ξt = 15/1144 and ξs = 0. Moreover, they represent a 35-fold and 20-fold improvement, respectively, over the joint analysis with only the isotropic 3PCF. We ensure the validity of our results by investigating various quantities, including theoretical models of the 3PCF, window function corrections, cumulative S/N, Fisher matrices, and statistical scattering effects of mock simulation data. We also find statistically significant discrepancies between the BOSS data and the Patchy mocks for the 3PCF measurement. Finally, we package all of our 3PCF analysis codes under the name hitomi and make them publicly available so that readers can reproduce all the results of this paper and easily apply them to ongoing future galaxy surveys.