Jensko, Erik;
(2023)
A unified approach to geometric modifications of gravity.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
This thesis studies modified theories of gravity from a geometric viewpoint. The primary motivation for considering alternatives to General Relativity comes from cosmological observations and theoretical arguments, which are discussed from the outset. Moreover, we explore the various different approaches to modifying gravity. We begin with an introduction of the mathematical foundations of General Relativity and gravitational theories in non-Riemannian geometries. Then, starting from the decomposition of the Einstein-Hilbert action into bulk and boundary terms, we construct new modifications of General Relativity. These modifications break diffeomorphism invariance or local Lorentz invariance, allowing one to bypass Lovelock's theorem while remaining second-order and without introducing additional fields. We work in both the Levi-Civita framework of General Relativity and the non-Riemannian metric-affine framework; the latter leads to a new Einstein-Cartan-type theory with propagating torsion. Important comparisons are also made with the modified teleparallel theories, and we construct a unified framework that encompasses all of these theories. The equivalence between theories that break fundamental symmetries in the Riemannian setting and non-Riemannian theories of gravity is explored in detail. This leads to a dual interpretation of teleparallel gravity, one in terms of geometric quantities and the other in terms of non-covariant objects. We then study the cosmological applications of these modified theories, making use of dynamical systems techniques. Strict conditions that models must satisfy in order to give rise to accelerated expansion (de Sitter solutions) are derived using these methods. Another key result is that the modified Einstein-Cartan theories can drive inflation in the early universe, replacing the initial cosmological singularity of General Relativity. To conclude, we discuss the viability of these modifications and possible future directions, examining their significance and relevance to the broader field of gravitational physics as a whole.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | A unified approach to geometric modifications of gravity |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2023. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10183387 |
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