Initial conditions for cold dark matter particles and General Relativity

Abstract

We describe the irrotational dust component of the universe in terms of a relativistic gradient expansion and transform the resulting synchronous metric to a Newtonian coordinate system. The two metrics are connected via a space-like displacement field and a time-like perturbation, providing a relativistic generalization of the transformation from Lagrangian to Eulerian coordinates. The relativistic part of the displacement field generates already at initial time a non-local density perturbation at second order. This is a purely relativistic effect since it originates from space-time mixing. We give two options, the passive and the active approach, on how to include the relativistic corrections for example in N-body simulations. In the passive approach we treat the corrections as a non-Gaussian modification of the initial Gaussian field (primordial non-Gaussianity could be incorporated as well). The induced non-Gaussianity depends on scale and the redshift at which initial conditions are set, with f_NL ~ few for small enough scales and redshifts. In the active approach we show how to use the relativistic trajectory to obtain the initial displacement and velocity of particles for N-body simulations without modifying the initial Gaussian field.

Title adjusted, added a table for clarity, matches published version

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Cited by in corpus (17)

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• Newton to Einstein - dust to dust
• Initial conditions for cosmological N-body simulations of the scalar sector of theories of Newtonian, Relativistic and Modified Gravity
• General Relativistic Cosmological N-body Simulations I: time integration
• Cosmological dynamics: from the Eulerian to the Lagrangian frame - I. Newtonian approximation
• A Relativistic view on large scale N-body simulations
• On the accuracy of N-body simulations at very large scales
• Astrophysical Bose-Einstein Condensates and Superradiance
• Constraint on dark matter central density in the Eddington inspired Born-Infeld (EiBI) gravity with input from Weyl gravity
• fNL - gNL mixing in the matter density field at higher orders
• On general-relativistic Lagrangian perturbation theory and its non-perturbative generalization
• Relativistic perturbations in $\Lambda$CDM: Eulerian & Lagrangian approaches
• Relativistic and non-Gaussianity contributions to the one-loop power spectrum