Detecting gravitational lensing by matter currents

TL;DR

This paper develops and validates a cross-correlation strategy to detect gravitomagnetic lensing from cosmological matter currents, a relativistic correction to standard lensing arising from mass motion. By reconstructing the cosmic momentum field from the galaxy density and cross-correlating it with the observed lensing convergence, the authors demonstrate a clean separation from the dominant scalar lensing signal, confirmed via N-body simulations. Forecasts indicate that upcoming wide-field surveys could achieve a statistically significant detection (S/N of order 5–10), providing the first cosmological probe of the large-scale momentum field and a direct test of general relativity and Lorentz invariance on cosmological scales. The study also assesses limitations from cosmic variance and explores variance-reduction strategies such as reconstructing the scalar convergence, outlining practical pathways to constrain gravitomagnetic effects in the near future.

Abstract

We explore the observational prospects for detecting gravitational lensing induced by cosmological matter currents, a relativistic correction to the standard scalar lensing effect arising from the motion of matter. We propose to isolate this contribution by cross-correlating the weak-lensing convergence field with a reconstructed cosmic momentum field inferred from galaxy surveys. Using numerical simulations, we demonstrate that this reconstructed momentum field is uncorrelated with the scalar 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.

Figures (4)

• Figure 1: Projected convergence fields constructed from the Quijote simulations using a snapshot geometry. Top: The scalar convergence field, $\kappa_{\Phi}$. Bottom: the momentum convergence field, $\kappa_{\parallel}$. Both images have been smoothed with a Gaussian filter.
• Figure 2: Left: the simulated gravitomagnetic field. Middle: the gravitomagnetic field reconstructed from the density field. Right: the difference between the gravitomagnetic field and the gravitomagnetic field reconstructed from the density field. Both fields have been smoothed using a Gaussian filter.
• Figure 3: The correlation coefficient $r(k)$ between each of the projected fields. The solid lines show the mean correlation coefficient from 15 different realisation of the fields (5 snapshost $\times$ 3 projection axes), the shaded regions show $1\sigma$ error bars calculated from the dispersion of the estimated correlation coefficients. Top: the correlation between the reconstructed momentum convergence $\hat{\kappa}_{j_{\parallel}}$ and the momentum convergence $\kappa_{j_{\parallel}}$. Middle: the correlation between the momentum convergence $\kappa_{j_{\parallel}}$ and the scalar convergence $\kappa_{\phi}$. Bottom: the correlation between the scalar convergence $\kappa_{\phi}$ and the reconstructed momentum convergence $\hat{\kappa}_{j_{\parallel}}$.
• Figure 4: Cumulative signal-to-noise ratio (S/N) forecasts for detecting the gravitomagnetic lensing signal as a function of maximum angular multipole $\ell$. All forecasts assume a sky fraction of $f_{\rm{sky}} \approx 0.25$. Left: the S/N for the cross-correlation of the lensing convergence with the reconstructed momentum convergence field for different galaxy number densities ($\bar{n}_g$, in units of Mpc$^{-3}$); solid lines show cosmic variance limited lensing noise, while dashed lines show Stage-4 lensing survey noise. Middle: the cosmic variance limited S/N for three different momentum field tracers: the true, noiseless field ($\kappa_{j){\parallel}}$), the reconstructed field ($\hat{\kappa}_{j){\parallel}}$) assuming a galaxy density of $\bar{n}_g = 10^-2$ Mpc$^-3$, and the kinetic Sunyaev-Zel'dovich (kSZ) effect. Right: the S/N for the cross-correlation after subtracting a reconstructed scalar convergence field ($\hat{\kappa}_{\phi}$), where the different lines show the effect of varying the galaxy density used for the scalar reconstruction.