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Volume 8
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10.3390/math8020290
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Article

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

by
Ivan Agullo
1,
Javier Olmedo
1,* and
Vijayakumar Sreenath
2
1
Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA
2
Department of Physics, National Institute of Technology Karnataka, Surathkal, Mangaluru 575025, India
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 290; https://doi.org/10.3390/math8020290
Submission received: 31 December 2019 / Revised: 4 February 2020 / Accepted: 15 February 2020 / Published: 20 February 2020
(This article belongs to the Special Issue Mathematical and Computational Cosmology)
Versions Notes

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 primordial perturbations; anisotropic spacetime; Hamiltonian formulation

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MDPI and ACS Style

Agullo, I.; Olmedo, J.; Sreenath, V. xAct Implementation of the Theory of Cosmological Perturbation in Bianchi I Spacetimes. Mathematics 2020, 8, 290. https://doi.org/10.3390/math8020290

AMA Style

Agullo I, Olmedo J, Sreenath V. xAct Implementation of the Theory of Cosmological Perturbation in Bianchi I Spacetimes. Mathematics. 2020; 8(2):290. https://doi.org/10.3390/math8020290

Chicago/Turabian Style

Agullo, Ivan, Javier Olmedo, and Vijayakumar Sreenath. 2020. "xAct Implementation of the Theory of Cosmological Perturbation in Bianchi I Spacetimes" Mathematics 8, no. 2: 290. https://doi.org/10.3390/math8020290

APA Style

Agullo, I., Olmedo, J., & Sreenath, V. (2020). xAct Implementation of the Theory of Cosmological Perturbation in Bianchi I Spacetimes. Mathematics, 8(2), 290. https://doi.org/10.3390/math8020290

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