A First Detection of the Connected 4-Point Correlation Function of Galaxies Using the BOSS CMASS Sample

Abstract

We present an 8.1σ detection of the non-Gaussian 4-Point Correlation Function (4PCF) using a sample of Ng ≈ 8 × 10 5 galaxies from the BOSS CMASS dataset. Our measurement uses the O(N 2 g ) NPCF estimator of , including a new modification to subtract the disconnected 4PCF contribution (arising from the product of two 2PCFs) at the estimator level. This approach is unlike previous work and ensures that our signal is a robust detection of gravitationally-induced non-Gaussianity. The estimator is validated with a suite of lognormal simulations, and the analytic form of the disconnected contribution is discussed. Due to the high dimensionality of the 4PCF, data compression is required; we use a signal-to-noise-based scheme calibrated from theoretical covariance matrices to restrict to ∼ 100 basis vectors. The compression has minimal impact on the detection significance and facilitates traditional χ 2 -like analyses using a suite of mock catalogs. The significance is stable with respect to different treatments of noise in the sample covariance (arising from the limited number of mocks), but decreases to 4.7σ when a minimum galaxy separation of 14 h −1 Mpc is enforced on the 4PCF tetrahedra (such that the statistic can be modelled more easily). The detectability of the 4PCF in the quasi-linear regime implies that it will become a useful tool in constraining cosmological and galaxy formation parameters from upcoming spectroscopic surveys.

Going Beyond the Galaxy Power Spectrum: an Analysis of BOSS Data with Wavelet Scattering Transforms

“…( 29) and for the BOSS CMASS dataset, as well as the PATCHY mocks, using Eq. (21). We highlight the excellent monopole agreement between the ABACUSSUMMIT prediction and the corresponding one from the data, down to scales smaller than the ones we work with in this analysis.…”

“…In order to fully exploit the additional gains associated with tapping into the nonlinear regime of the LSS, one thus needs to evaluate higher-order statistics beyond the 2-point function. Despite significant theoretical progress made towards this direction in the past decade [15][16][17][18][19][20][21], including higher-order moments as part of a standard parameter inference scheme quickly becomes intractable, both from a computational standpoint, because of the sharply rising dimensionality of the resulting data vector, but also on the theoretical modeling front. In addition, in more challenging cases, such as that of a probability distribution with a heavy tail, even a complete description of all moments would fail to capture all available information, while at the same time amplifying outliers by raising the density field to very high powers [14].…”

Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies

“…Another promising avenue is via the inclusion of higher-order statistics, such as the galaxy trispectrum or fourpoint correlation function and beyond. Initial forecasts suggest that the statistics can yield impressive constraining power on σ 8 [1857], arising due to degeneracy breaking, and recently, the first detections of such quantities have been made [1858,1859]. Of course, their use will require the development of rigorous theoretical models [1860] that must be tested on simulations (including systematic effects) before their application to data.…”

The Power of Locality: Primordial Non-Gaussianity at the Map Level

“…This strategy has been successfully employed on current BOSS data to measure cosmological parameters using the power spectrum [78][79][80] and bispectrum [80][81][82][83][84]. In principle, one can imagine measuring successively higher-order correlators [85,86] to extract additional information from the maps and we anticipate that higher-point information will become increasingly valuable with larger surveys [87][88][89].…”