Second-order cosmological perturbation theory and initial conditions for $N$-body simulations

Abstract

We use gauge-invariant cosmological perturbation theory to calculate the displacement field that sets the initial conditions for $N$-body simulations. Using first and second-order fully relativistic perturbation theory in the synchronous-comoving gauge, allows us to go beyond the Newtonian predictions and to calculate relativistic corrections to it. We use an Einstein--de Sitter model, including both growing and decaying modes in our solutions. The impact of our results should be assessed through the implementation of the featured displacement in cosmological $N$-body simulations.

V2: Second order density added and other expressions simplified. References updated. 15 pages

References in corpus (6)

• Transients from Initial Conditions in Cosmological Simulations
• N-body methods for relativistic cosmology
• Can cosmological perturbations produce early universe vorticity?
• Relativistic Lagrangian displacement field and tensor perturbations
• Modelling non-dust fluids in cosmology
• A Relativistic view on large scale N-body simulations

Cited by in corpus (12)

• Relativistic Interpretation of Newtonian Simulations for Cosmic Structure Formation
• Cosmology on all scales: a two-parameter perturbation expansion
• General relativistic 'screening' in cosmological simulations
• Non-Spherical Szekeres models in the language of Cosmological Perturbations
• Lagrangian theory for cosmic structure formation with vorticity: Newtonian and post-Friedmann approximations
• General Relativistic Cosmological N-body Simulations I: time integration
• Interactive mixture of inhomogeneous dark fluids driven by dark energy: a dynamical systems analysis
• Second order cosmological perturbations: new conserved quantities and the general solution at super-horizon scale
• Isocurvature initial conditions for second order Boltzmann solvers
• Including relativistic and primordial Non-Gaussianity contributions in cosmological simulations by modifying the initial condition
• Relativistic and non-Gaussianity contributions to the one-loop power spectrum
• The Effect of Corner Modes in the Initial Conditions of Cosmological Simulations