Nonlinear general relativistic corrections to redshift space distortions, gravitational lensing magnification and cosmological distances
2012
The next generation of telescopes will usher in an era of precision cosmology, capable of determining the cosmological model to percent level and beyond. 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-
redshiftrelation to second order in
cosmological perturbation theory. This
relationdetermines the magnification of sources at high precision, as well as nonlinear aspects of
redshift space distortions. We identify a range of new lensing effects, including:
double-integratedand nonlinear integrated Sach-Wolfe contributions, transverse
Doppler effectsin
redshift space distortions, lensing from the induced vector mode and
gravitational wave backgrounds, in addition to lensing from the second-order potential. Finally, we identify 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 in certain situations, and so offer important new probes of gravitational lensing.
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