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Title: The Poisson equation at second order in relativistic cosmology

We calculate the relativistic constraint equation which relates the curvature perturbation to the matter density contrast at second order in cosmological perturbation theory. This relativistic ''second order Poisson equation'' is presented in a gauge where the hydrodynamical inhomogeneities coincide with their Newtonian counterparts exactly for a perfect fluid with constant equation of state. We use this constraint to introduce primordial non-Gaussianity in the density contrast in the framework of General Relativity. We then derive expressions that can be used as the initial conditions of N-body codes for structure formation which probe the observable signature of primordial non-Gaussianity in the statistics of the evolved matter density field.
Authors:
 [1] ;  [2] ;  [3]
  1. Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 3FX (United Kingdom)
  2. School of Physics and Astronomy, University of Nottingham, University Park, Nottingham, NG7 2RD (United Kingdom)
  3. Astronomy Unit, School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London, E1 4NS (United Kingdom)
Publication Date:
OSTI Identifier:
22282718
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2013; Journal Issue: 08; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COSMOLOGY; DENSITY; EQUATIONS OF STATE; GENERAL RELATIVITY THEORY; LIMITING VALUES; PERTURBATION THEORY; POISSON EQUATION; RELATIVISTIC RANGE