Detecting gravitational lensing by matter currents

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.