xAct Implementation of the Theory of Cosmological Perturbation in Bianchi I Spacetimes

TL;DR

This paper introduces a computational algorithm using xAct packages to derive gauge-invariant linear perturbations in anisotropic Bianchi I cosmological spacetimes, facilitating analysis of their dynamics.

Contribution

The paper develops a Hamiltonian-based algorithm implemented in xAct to efficiently derive gauge-invariant perturbations in Bianchi I spacetimes, extending previous methods.

Findings

Provides a new computational tool for anisotropic cosmological perturbations.

Enables transparent isolation of gauge-invariant degrees of freedom.

Facilitates analysis of perturbations in Bianchi I models.

Abstract

This paper presents a computational algorithm to derive the theory of linear gauge invariant perturbations on anisotropic cosmological spacetimes of the Bianchi I type. Our code is based on the tensor algebra packages xTensor and xPert, within the computational infrastructure of xAct written in Mathematica. The algorithm is based on a Hamiltonian, or phase space formulation, and it provides an efficient and transparent way of isolating the gauge invariant degrees of freedom in the perturbation fields and to obtain the Hamiltonian generating their dynamics. The restriction to Friedmann--Lema\^itre--Robertson--Walker spacetimes is straightforward.