Weak-lensing by the large scale structure in a spatially anisotropic
  universe: theory and predictions
  This article details the computation of the two-point correlators of the
convergence, $E$- and $B$-modes of the cosmic shear induced by the weak-lensing
by large scale structure assuming that the background spacetime is spatially
homogeneous and anisotropic. After detailing the perturbation equations and the
general theory of weak-lensing in an anisotropic universe, it develops a weak
shear approximation scheme in which one can compute analytically the evolution
of the Jacobi matrix. It allows one to compute the angular power spectrum of
the $E$- and $B$-modes. In the linear regime, the existence of $B$-modes is a
direct tracer of a late time anisotropy and their angular power spectrum scales
as the square of the shear. It is then demonstrated that there must also exist
off-diagonal correlations between the $E$-modes, $B$-modes and convergence that
are linear in the geometrical shear and allow one to reconstruct the
eigendirections of expansion. These spectra can be measured in future large
scale surveys, such as Euclid and SKA, and offer a new tool to test the
isotropy of the expansion of the universe at low redshift.
