xAct Implementation of the Theory of Cosmological Perturbation in Bianchi I Spacetimes
arXiv:2006.03397 · doi:10.3390/math8020290
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--Lemaître--Robertson--Walker spacetimes is straightforward.
20 pages, references added and updated
References in corpus (8)
- xPert: Computer algebra for metric perturbation theory
- Theory of cosmological perturbations in an anisotropic universe
- Predictions from an anisotropic inflationary era
- Cosmological perturbations in Hybrid Loop Quantum Cosmology: Mukhanov-Sasaki variables
- A complete gauge-invariant formalism for arbitrary second-order perturbations of a Schwarzschild black hole
- Second and higher-order perturbations of a spherical spacetime
- Hamiltonian theory of classical and quantum gauge invariant perturbations in Bianchi I spacetimes
- High-order perturbations of a spherical collapsing star
Cited by in corpus (4)
- Observational consequences of Bianchi I spacetimes in loop quantum cosmology
- QFT in Curved Spacetime from Quantum Gravity: proper WKB decomposition of the gravitational component
- Loop quantum cosmology: relation between theory and observations
- Observational constraints on anisotropies for bouncing alternatives to inflation