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The significant increase in precision that will be achieved by Stage IVcosmic shear surveys means that several currently used theoreticalapproximations may cease to be valid. An additional layer of complexity arisesfrom the fact that many of these approximations are interdependent; theprocedure to correct for one involves making another. Two such approximationsthat must be relaxed for upcoming experiments are the reduced shearapproximation and the effect of neglecting magnification bias. Accomplishingthis involves the calculation of the convergence bispectrum; typically subjectto the Limber approximation. In this work, we compute the post-Limberconvergence bispectrum, and the post-Limber reduced shear and magnificationbias corrections to the angular power spectrum for a Euclid-like survey. Wefind that the Limber approximation significantly overestimates the bispectrumwhen any side of the bispectrum triangle, $\ell_i<60$. However, the resultingchanges in the reduced shear and magnification bias corrections are well belowthe sample variance for $\ell\leq5000$. We also compute a worst-case scenariofor the additional biases on $w_0w_a$CDM cosmological parameters that resultfrom the difference between the post-Limber and Limber approximated forms ofthe corrections. These further demonstrate that the reduced shear andmagnification bias corrections can safely be treated under the Limberapproximation for upcoming surveys.

Post-Limber Weak Lensing Bispectrum, Reduced Shear Correction, and Magnification Bias Correction