Detecting gravitational lensing by matter currents

¹ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191, Gif-sur-Yvette, France
² Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013, Paris, France
³ Department of Physics & Astronomy, University of Sussex, Brighton BN1 9QH, U.K.
⁴ CNRS-UCB International Research Laboratory, Centre Pierre Binétruy, IRL2007, CPB-IN2P3, Berkeley, USA

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 22 October 2025
Accepted: 10 February 2026

Abstract

We explored the observational prospects for detecting gravitational lensing induced by cosmological matter currents, a relativistic correction to the standard density lensing effect arising from the motion of matter. We propose isolating this contribution by cross-correlating the weak-lensing convergence field with a reconstructed cosmic momentum field inferred from galaxy redshift surveys. Using numerical simulations, we demonstrate that this reconstructed momentum field is uncorrelated with the density lensing signal, enabling a clean separation of the gravitomagnetic component. We then forecast the detectability of this signal for upcoming wide-field galaxy and weak-lensing surveys, showing that a statistically significant detection may be achievable under realistic observational conditions. Such a measurement would provide the first direct probe of the large-scale cosmic momentum field, offering a novel test of general relativity and Lorentz invariance on cosmological scales.