Non-linear relativistic contributions to the cosmological weak-lensing
  convergence
  Relativistic contributions to the dynamics of structure formation come in a
variety of forms, and can potentially give corrections to the standard picture
on typical scales of 100 Mpc. These corrections cannot be obtained by Newtonian
numerical simulations, so it is important to accurately estimate the magnitude
of these relativistic effects. Density fluctuations couple to produce a
background of gravitational waves, which is larger than any primordial
background. A similar interaction produces a much larger spectrum of vector
modes which represent the frame-dragging rotation of spacetime. These can
change the metric at the percent level in the concordance model at scales below
the equality scale. Vector modes modify the lensing of background galaxies by
large-scale structure. This gives in principle the exciting possibility of
measuring relativistic frame dragging effects on cosmological scales. The
effects of the non-linear tensor and vector modes on the cosmic convergence are
computed and compared to first-order lensing contributions from density
fluctuations, Doppler lensing, and smaller Sachs-Wolfe effects. The lensing
from gravitational waves is negligible so we concentrate on the vector modes.
We show the relative importance of this for future surveys such as Euclid and
SKA. We find that these non-linear effects only marginally affect the overall
weak lensing signal so they can safely be neglected in most analyses, though
are still much larger than the linear Sachs-Wolfe terms. The second-order
vector contribution can dominate the first-order Doppler lensing term at
moderate redshifts and are actually more important for survey geometries like
the SKA.
