Nonlinear relativistic corrections to cosmological distances, redshift
  and gravitational lensing magnification. I - Key results
  The next generation of telescopes will usher in an era of precision
cosmology, capable of determining the cosmological model to beyond the percent
level. For this to be effective, the theoretical model must be understood to at
least the same level of precision. A range of subtle relativistic effects
remain to be explored theoretically, and offer the potential for probing
general relativity in this new regime. We present the distance-redshift
relation to second order in cosmological perturbation theory for a general dark
energy model. This relation determines the magnification of sources at high
precision, as well as redshift space distortions in the mildly non-linear
regime. We identify a range of new lensing effects, including:
double-integrated and nonlinear integrated Sach-Wolfe contributions, transverse
Doppler effects, lensing from the induced vector mode and gravitational wave
backgrounds, in addition to lensing from the second-order potential.
Modifications to Doppler lensing from redshift-space distortions are
identified. Finally, we find a new double-coupling between the density
fluctuations integrated along the line of sight, and gradients in the density
fluctuations coupled to transverse velocities along the line of sight. These
can be large and thus offer important new probes of gravitational lensing and
general relativity. This paper accompanies arXiv:1402.1933, where a
comprehensive derivation is given.
