Relativistic weak lensing from a fully non-linear cosmological density field

D. B. Thomas, M. Bruni, D. Wands

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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.
Original languageEnglish
Article number021
JournalJournal of Cosmology and Astroparticle Physics
Issue number9
Publication statusPublished - 8 Sept 2015


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


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