The Poisson equation at second order in relativistic cosmology

Abstract

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 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.

V2: New appendix shows consistency with previous work. Matches version accepted by JCAP

References in corpus (9)

• The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects
• Transients from Initial Conditions in Cosmological Simulations
• Non-gaussianity from the second-order cosmological perturbation
• Scale-dependent bias from primordial non-Gaussianity in general relativity
• The intrinsic bispectrum of the Cosmic Microwave Background [PhD thesis]
• The CMB bispectrum from recombination
• A Concise Introduction to Perturbation Theory in Cosmology
• Modelling non-dust fluids in cosmology
• Scale-dependent bias from multiple-field inflation

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