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

Ivan Agullo, Javier Olmedo and Vijayakumar Sreenath
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Ivan Agullo: Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA
Javier Olmedo: Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA
Vijayakumar Sreenath: Department of Physics, National Institute of Technology Karnataka, Surathkal, Mangaluru 575025, India

Mathematics, 2020, vol. 8, issue 2, 1-19

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.

Keywords: primordial perturbations; anisotropic spacetime; Hamiltonian formulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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