Cosmic shear bispectrum from second-order perturbations in general relativity

Abstract

Future lensing surveys will be nearly full sky and reach an unprecedented depth, probing scales closer and closer to the Hubble radius. This motivates the study of the cosmic shear beyond the small-angle approximation, including general relativistic corrections that are usually suppressed on sub-Hubble scales. The complete expression of the reduced cosmic shear at second order including all relativistic effects was derived in [F. Bernardeau, C. Bonvin, and F. Vernizzi, Phys. Rev. D 81, 083002 (2010).]. In the present paper we compute the resulting cosmic shear bispectrum when all these effects are properly taken into account and we compare it to primordial non-Gaussianity of the local type. The new general relativistic effects are generically smaller than the standard nonlinear couplings. However, their relative importance increases at small multipoles and for small redshifts of the sources. The dominant effect among these nonstandard corrections is due to the inhomogeneity of the source redshift. In the squeezed limit, its amplitude can become of the order of the standard couplings when the redshift of the sources is below 0.5. Moreover, while the standard nonlinear couplings depend on the angle between the short and long mode, the relativistic corrections do not and overlap almost totally with local type non-Gaussianity. We find that they can contaminate the search for a primordial local signal by ${f}_{\mathrm{NL}}^{\mathrm{loc}}\ensuremath{\gtrsim}10$.