Weak Lensing Low Multipoles

Abstract

We analyse the low--multipole components of the weak-lensing convergence field in a FLRW universe. The low--multipole convergence field, encodes the largest-angle coherent potential gradients, essential for assessment of large-angle features in data. To study this large angle signal, we perform a combined analytical, numerical and observational study. Starting from exact analytical expressions for the convergence power spectrum, we quantify how the dipole, quadrupole and octupole build up with source redshift and show that, in $Λ$CDM, they saturate at an amplitude of order $10^{-4}$. We then use full-sky, horizon-scale $N$-body simulations (Quijote) to explore the dependence of this signal on the observer's environment, comparing random observers to ``Milky Way--like'' observers. In parallel, we reconstruct the convergence field due to our local Universe with the 2MASS Redshift Survey (2MRS), with proper treatment of incompleteness and galaxy bias. We find that the observed low multipoles from observation is above the $Λ$CDM mean predictions, but in full agreement with Milky Way--like observers in the simulation. Finally, by converting the convergence dipole into a number-count dipole, we test whether weak lensing can contribute to the cosmic dipole anomaly, an idea motivated by its natural alignment with the CMB dipole and by the fact that lensing, unlike clustering, cannot be removed by cross-matching surveys and thus survives in all high-redshift catalogues. We show that weak lensing by local structure contributes at most a few percent to this observed anomaly.