## Abstract

In this paper we examine cosmological weak lensing on non-linear scales and

show that there are Newtonian and relativistic contributions and that the latter can also be extracted from standard Newtonian simulations. We use the post-Friedmann formalism, a post-Newtonian type framework for cosmology, to derive the full weak-lensing deflection angle valid on non-linear scales for any metric theory of gravity. We show that the only contributing term that is quadratic in the first order deflection is the expected Born correction and lens-lens coupling term. We use this deflection angle to analyse the vector and tensor contributions to the E- and B- mode cosmic shear power spectra. In our approach, once the gravitational theory has been specified, the metric components are related to the matter content in a welldefined manner. Specifying General Relativity, we write down a complete set of equations for

a GR+CDM universe for computing all of the possible lensing terms from Newtonian Nbody simulations. We illustrate this with the vector potential and show that, in a GR+CDM universe, its contribution to the E-mode is negligible with respect to that of the conventional Newtonian scalar potential, even on non-linear scales. Thus, under the standard assumption that Newtonian N-body simulations give a good approximation of the matter dynamics, we show that the standard ray tracing approach gives a good description for a CDM cosmology.

show that there are Newtonian and relativistic contributions and that the latter can also be extracted from standard Newtonian simulations. We use the post-Friedmann formalism, a post-Newtonian type framework for cosmology, to derive the full weak-lensing deflection angle valid on non-linear scales for any metric theory of gravity. We show that the only contributing term that is quadratic in the first order deflection is the expected Born correction and lens-lens coupling term. We use this deflection angle to analyse the vector and tensor contributions to the E- and B- mode cosmic shear power spectra. In our approach, once the gravitational theory has been specified, the metric components are related to the matter content in a welldefined manner. Specifying General Relativity, we write down a complete set of equations for

a GR+CDM universe for computing all of the possible lensing terms from Newtonian Nbody simulations. We illustrate this with the vector potential and show that, in a GR+CDM universe, its contribution to the E-mode is negligible with respect to that of the conventional Newtonian scalar potential, even on non-linear scales. Thus, under the standard assumption that Newtonian N-body simulations give a good approximation of the matter dynamics, we show that the standard ray tracing approach gives a good description for a CDM cosmology.

Original language | English |
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Article number | 021 |

Journal | Journal of Cosmology and Astroparticle Physics |

Volume | 2015 |

Issue number | 9 |

DOIs | |

Publication status | Published - 8 Sept 2015 |

## Keywords

- gravitational lensing
- gravity
- STFC
- RCUK
- ST/H002774/1
- ST/L005573/1
- ST/K00090X/1