http://arxiv.org/abs/1402.1933
We present a derivation of the cosmological distance-redshift relation up to second order in perturbation theory. In addition, we find the observed redshift and the lensing magnification to second order. Since we do not use the field or conservation equations, we do not require that the density contrast is small, only that the metric potentials and peculiar velocities are small. Thus our results apply into the nonlinear regime, and can be used for most dark energy models. We present the results in a form which can be readily computed in an N-body simulation. This paper accompanies arXiv:1207.2109, where the key results are summarised and discussed.
O. Umeh, C. Clarkson and R. Maartens
Tue, 11 Feb 14
34/55
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