Advances in upcoming weak lensing surveys pose new challenges for an accurate modeling of the lensing observables. With their large sky coverage, common approximations based on a flat-sky geometry cannot be used anymore to evaluate all measurable angular scales. Moreover, additional relativistic effects manifest themselves on large scales and thus need to be accounted for. In particular, the lensing magnification cannot be correctly described by the standard lensing convergence only. We present the analytical solutions for the fully-relativistic weak lensing angular power spectra, including the contribution from primordial gravitational waves. We compare the results obtained by using the Limber approximation with the precise all-sky calculations using spherical harmonics. Our numerical evaluations show that general relativistic corrections are one order-of-magnitude below cosmic variance at small scales ($lgeq 10$). At large scales ($l<10$), however, neglecting them leads to more significant errors, especially when combined with the Limber approximation. Hence, a precise, fully-relativistic modeling is necessary at these largest scales.
تحميل البحث