The detection of a non-Gaussian signature in the early Universe would be a smoking gun for many inflation models. Despite a number of searches, no evidence has been found for primordial non-Gaussianity in the Cosmic Microwave Background (CMB). Now, Oliver Philcox and colleagues for the first time reported the detection of the non-Gaussian 4 point-correlation function of Galaxies using the BOSS CMASS sample. Their study published in *Arxiv* on 3 Aug 2021.

What makes this detection possible, is the use of an estimator which was recently presented by Oliver Philcox et al. for computing the N-point galaxy correlation functions of Ng galaxies in O(Ng^2) time and a new modification to subtract the disconnected 4PCF contribution (arising from the product of two 2PCFs) at the estimator level.

“This is unlike previous works, and ensures that our measurement is specifically one of non-Gaussianity, rather than a recapitulation of known physics. The estimator is fast (scaling quadratically with the galaxy number density), corrected for the non-uniform survey geometry, and implemented in the public encore code. We verify its performance on a suite of lognormal simulations at high redshift, before applying it to the BOSS dataset and Patchy simulations.”

Additionally, analysis of the higher-point functions like 4PCF is hampered by their high dimension; so they have to implement a signal-to-noise-based compression scheme, which allows them to project the 4PCF into a set of ∼ 50 numbers with minimal impact on the detection significance.

“The compression has minimal impact on detection significance and facilitates traditional classical χ²-like analysis using a suite of mock catalogs”

Finally, by performing a classical χ²-like analysis in the compressed subspace they detected an 8.1σ of the non-Gaussian 4PCF.

“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.”

— they concluded.

Analysis code for the BOSS Even-Parity 4PCF Analysis using encore is available at: https://github.com/oliverphilcox/Parity-Even-4PCF

**References***: (1) Oliver H. E. Philcox, Zachary Slepian, Jiamin Hou, Craig Warner, Robert N. Cahn, Daniel J. Eisenstein, “ENCORE: Estimating Galaxy N-point Correlation Functions in O(N2g) Time”, Arxiv, pp. 1-24, 2021. **https://arxiv.org/abs/2105.08722** (2) Oliver H. E. Philcox, Jiamin Hou, and Zachary Slepian, “A First Detection of the Connected 4-Point Correlation Function of Galaxies Using the BOSS CMASS Sample”, Arxiv, pp. 1-26, 2021. **arXiv:2108.01670*

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