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Looking for a twist: probing the cosmological gravitomagnetic effect via weak lensing-kSZ cross correlations

Barrera-Hinojosa, Cristian; Li, Baojiu; Cai, Yan-Chuan

Looking for a twist: probing the cosmological gravitomagnetic effect via weak lensing-kSZ cross correlations Thumbnail


Cristian Barrera-Hinojosa

Yan-Chuan Cai


General relativity predicts that the rotational momentum flux of matter twists the space–time via a vector gravitomagnetic (frame-dragging) field, which remains undetected in cosmology. This vector field induces an additional gravitational lensing effect; at the same time, the momentum field sources the kinetic Sunyaev–Zel’dovich (kSZ) effect. The common origin of these two effects allows us to probe the gravitomagnetic signal via their cross-correlations. In this paper, we explore the possibility of detecting the gravitomagnetic field in Λ cold dark matter by cross-correlating the weak-lensing convergence field with the cosmic microwave background (CMB) temperature map, which is imprinted with the kSZ signal. This approach allows us to extract the gravitomagnetic effect because the cross-correlation between the standard Newtonian contribution to the weak-lensing convergence field, κΦ⁠, and the kSZ effect is expected to vanish. We study the cross-correlations with a suite of large-volume Newtonian N-body simulations and a small-volume, high-resolution, general-relativistic counterpart. We show that insufficient simulation resolution can introduce significant spurious correlations between κΦ and kSZ. From the high-resolution simulation, we find that the cumulative signal-to-noise ratio (SNR) of the kSZ-gravitomagnetic convergence field can reach almost 15 (30) at ℓ ≃ 5000 (104) for the lensing source redshift zs = 0.83, if only cosmic variance is considered. We make forecast for next-generation lensing surveys such as EUCLID and LSST, and CMB experiments such as Simons Observatory and CMB-S4, and find that, for zs = 1.4, the cumulative SNR can exceed 5 (9) at ℓ ≃ 5000 (104), indicating that the cosmological gravitomagnetic effect can be detected, if several foreground contaminations can be removed.

Journal Article Type Article
Acceptance Date Dec 8, 2021
Online Publication Date Dec 20, 2021
Publication Date 2022-03
Deposit Date Oct 27, 2021
Publicly Available Date Jun 14, 2022
Journal Monthly Notices of Royal Astronomical Society
Print ISSN 0035-8711
Electronic ISSN 1365-2966
Publisher Royal Astronomical Society
Peer Reviewed Peer Reviewed
Volume 510
Issue 3
Pages 3589-3604
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Copyright Statement
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
© The Author(s) 2021. Published by Oxford University Press on behalf of Royal Astronomical Society.

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