Post-Newtonian cosmological dynamics of plane-parallel perturbations and back-reaction

Understand

We study the general relativistic non-linear dynamics of self-gravitating irrotational dust in a cosmological setting, adopting the comoving and synchronous gauge, where all the equations can be written in terms of the metric tensor of spatial hyper-surfaces orthogonal to the fluid flow.

• Performing an expansion in inverse powers of the speed of light, we obtain the post-Newtonian equations, which yield the lowest-order relativistic effects arising during the non-linear evolution.
• We then specialize our analysis to globally plane-parallel configurations, i.e.
• to the case where the initial perturbation field depends on a single coordinate.