Weak lensing B modes on all scales as a probe of local isotropy

This article introduces a new multipolar hierarchy for the propagation of the weak-lensing shear, convergence, and twist valid in a general spacetime. Our approach is fully covariant and relies on no perturbative expansion. We show that the origin of B modes, in particular on large angular scales, is related to deviations of isotropy of the spacetime. Known results assuming a Friedmann-Lemaitre background spacetime are naturally recovered. The example of a Bianchi I spacetime illustrates our formalism and its implications for future observations are stressed. DOI: 10.1103/PhysRevD.87.043003