General Relativistic Effects in Weak Lensing Angular Power Spectra

Abstract: Advances in upcoming weak lensing surveys pose new challenges for an accurate modeling of the lensing observables. The wide sky coverage of Euclid makes angular scales down to $l_\mathrm{min}=10$ accessible. At such large angular scales, general relativistic effects manifest themselves, and the lensing magnification cannot be correctly described by the standard lensing convergence only. The impact of line-of-sight velocities on the magnification angular power spectrum, referred to as the Doppler magnification, is already well recognized in literature. In particular, it was suggested that the Doppler magnification could be extracted by measurements of both cosmic shear and magnification. In this work, we point out two previously neglected aspects with respect to this method. Firstly, the impact of the Doppler magnification is reduced through non-vanishing cross terms with the standard lensing convergence. This is particularly relevant when the sources are averaged over a bin of width $\Delta z\approx 0.1$, such as in Euclid's tomographic weak lensing survey. Secondly, general relativistic potential terms slightly enhance the signal. We present numerical calculations of all relativistic effects in the weak lensing angular power spectra on large scales.