Nonlinear relativistic corrections to cosmological distances, redshift and gravitational lensing magnification. I - Key results

TL;DR

This paper develops a second-order relativistic correction framework for cosmological distance and lensing measurements, enabling high-precision tests of general relativity with upcoming telescopic data.

Contribution

It introduces a comprehensive second-order perturbation theory model for cosmological distances, including new lensing effects and couplings, advancing the theoretical understanding for precision cosmology.

Findings

Identified new lensing effects such as double-integrated Sachs-Wolfe contributions.

Derived second-order corrections to the distance-redshift relation.

Revealed large double-coupling effects between density fluctuations and velocities.

Abstract

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.