Obinna Umeh, Chris Clarkson, Roy Maartens
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-redshift relation to second order in cosmological perturbation theory. This relation determines 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-integrated and nonlinear integrated Sach-Wolfe contributions, transverse Doppler effects in 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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http://arxiv.org/abs/1207.2109
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