xPand: An algorithm for perturbing homogeneous cosmologies

Understand

In this paper, we develop in detail a fully geometrical method for deriving perturbation equations about a spatially homogeneous background.

• This method relies on the 3+1 splitting of the background space-time and does not use any particular set of coordinates: it is implemented in terms of geometrical quantities only, using the tensor algebra package xTensor in the xAct distribution along with the extension for perturbations xPert.
• Our algorithm allows one to obtain the perturbation equations for all types of homogeneous cosmologies, up to any order and in all possible gauges.
• As applications, we recover the well-known perturbed Einstein equations for Friedmann-Lemaitre-Robertson-Walker cosmologies up to second order and for Bianchi I cosmologies at first order.