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The detection of the imprint of filaments on cosmic microwave background lensing


Galaxy redshift surveys, such as the 2-Degree-Field Survey (2dF)1, Sloan Digital Sky Survey (SDSS)2, 6-Degree-Field Survey (6dF)3, Galaxy And Mass Assembly survey (GAMA)4 and VIMOS Public Extragalactic Redshift Survey (VIPERS)5, have shown that the spatial distribution of matter forms a rich web, known as the cosmic web6. Most galaxy survey analyses measure the amplitude of galaxy clustering as a function of scale, ignoring information beyond a small number of summary statistics. Because the matter density field becomes highly non-Gaussian as structure evolves under gravity, we expect other statistical descriptions of the field to provide us with additional information. One way to study the non-Gaussianity is to study filaments, which evolve non-linearly from the initial density fluctuations produced in the primordial Universe. In our study, we report the detection of lensing of the cosmic microwave background (CMB) by filaments, and we apply a null test to confirm our detection. Furthermore, we propose a phenomenological model to interpret the detected signal, and we measure how filaments trace the matter distribution on large scales through filament bias, which we measure to be around 1.5. Our study provides new scope to understand the environmental dependence of galaxy formation. In the future, the joint analysis of lensing and Sunyaev–Zel’dovich observations might reveal the properties of ‘missing baryons’, the vast majority of the gas that resides in the intergalactic medium, which has so far evaded most observations.

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Fig. 1: The filament length as a function of redshift.
Fig. 2: Cross angular power spectrum.
Fig. 3: Relationship between filament map and galaxy map.


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We thank A. Pullen and E. Giusarma for discussion, M. White for providing us with the N-body simulations, and A. Krolewski and B. Horowitz for comments on the draft. S. Ho is supported by NASA and DOE for this work. S. He is supported by NSF-AST1517593 for this work. S.A. is supported by the European Research Council through the COSFORM Research Grant (#670193). S.F. thanks the Miller Institute for Basic Research in Science at the University of California, Berkeley for support. Some of the results in this paper have been derived using the HEALPix package. The authors would like to acknowledge the support of NERSC.

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Authors and Affiliations



S. He led the project and most of the manuscript writing. S.A. provided the sky mocks for galaxies and dark matter particles as well as wrote the text relative to sky mock for Filaments and Dark Matter in the Method section. S.F. helped with the theoretical modelling and the interpretation of the results, as well as writing part of the manuscript. Y.C. provided the filament intensity maps for data and simulations. S.Ho conceived the idea of cross-correlating filaments with CMB lensing. All authors contributed to the interpretation of the data and commented on the manuscript.

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Correspondence to Siyu He.

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He, S., Alam, S., Ferraro, S. et al. The detection of the imprint of filaments on cosmic microwave background lensing. Nat Astron 2, 401–406 (2018).

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