Journal Article

Zel’dovich approximation and general relativity

Cornelius Rampf and Gerasimos Rigopoulos

in Monthly Notices of the Royal Astronomical Society: Letters

Published on behalf of The Royal Astronomical Society

Volume 430, issue 1, pages L54-L58
Published in print March 2013 |
Published online December 2012 | e-ISSN: 1745-3933 | DOI:

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We show how the Zel’dovich approximation and the second-order displacement field of Lagrangian perturbation theory can be obtained from a general relativistic gradient expansion in Λ cold dark matter cosmology. The displacement field arises as a result of a second-order non-local coordinate transformation which brings the synchronous/comoving metric into a Newtonian form. We find that, with a small modification, the Zel’dovich approximation holds even on scales comparable to the horizon. The corresponding density perturbation is not related to the Newtonian potential via the usual Poisson equation but via a modified Helmholtz equation. This is a consequence of causality not present in the Newtonian theory. The second-order displacement field receives relativistic corrections that are subdominant on short scales but are comparable to the second-order Newtonian result on scales approaching the horizon. The corrections are easy to include when setting up initial conditions in large N-body simulations.

Keywords: cosmology: theory; dark matter; large-scale structure of Universe

Journal Article.  3674 words. 

Subjects: Astronomy and Astrophysics

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