Initial conditions for cold dark matter particles and General Relativity

Understand

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.