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Influence of topology in inhomogeneous cosmology through non-Euclidean extensions of Newton’s theory and relativistic numerical schemes

Abstract : The Standard Model of Cosmology assumes that the small scale inhomogeneities do not affect the expansion of the largest scales. However, such a phenomenon, named \textit{backreaction}, could exist and be important enough to explain the dark energy. While most of the studies about the backreaction focused on its relation with structure formation, little has been made to understand its dependence on the topology of our Universe. My PhD thesis aims at filling this gap, following two strategies. Firstly, I try to define a non-Euclidean extension of Newton's theory from general relativity and to generalise the \BET, which states that the backreaction is zero in Newton's theory. As a first step towards this definition I show that the Newtonian cosmology can be derived from the Newton-Cartan theory. In this case, the expansion arises as a fundamental field of the theory. I then propose two `non-Euclidean Newtonian theories' based on the Newton-Cartan formalism. The first theory features a backreaction, while the other features none. Finally I try to justify one of them using the Galilean limit of general relativity. I show that to allow for non-Euclidean geometries at the limit, an additional term related to the spatial curvature needs to be added to the energy-momentum tensor of a geodesic fluid. One of the consequence of this modification is that the system of equations at leading order is not closed, leaving open the question of the `right' non-Euclidean Newtonian theory compatible with general relativity. Secondly, I study the possibility of making relativistic cosmological simulations in non-Euclidean geometries. Relativistic simulations are starting to be used as new independent methods to quantify the backreaction. However, until now they have all been done in an Euclidean geometry, and have all relied on the BSSN formalism to solve the Einstein equation. I show that this numerical scheme might not be adapted to non-Euclidean geometries and I suggest to use its covariant version.
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https://tel.archives-ouvertes.fr/tel-03481716
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Submitted on : Wednesday, December 15, 2021 - 2:44:07 PM
Last modification on : Tuesday, January 4, 2022 - 6:45:11 AM
Long-term archiving on: : Wednesday, March 16, 2022 - 7:06:13 PM

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Quentin Vigneron. Influence of topology in inhomogeneous cosmology through non-Euclidean extensions of Newton’s theory and relativistic numerical schemes. Cosmology and Extra-Galactic Astrophysics [astro-ph.CO]. Université de Lyon, 2021. English. ⟨NNT : 2021LYSE1117⟩. ⟨tel-03481716⟩

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