- 203-1-2161 Thermodynamics And Statistical Mechanics 1 (Teaching assistant), 2024A
- 203-1-4181 Gravitation Theory 1 (Teaching assistant), 2024A
The Weak Gravity Conjecture in de-Sitter Space
with Eran Palti
Abstract/Description: This thesis delves into the intriguing realm of the Weak Gravity Conjecture (WGC) within the context of de Sitter space. The WGC, a fundamental principle in the landscape of theoretical physics, posits that gravity is always the weakest force in any consistent quantum field theory. While extensively studied in flat and anti-de Sitter spacetimes, its implications and applicability in de Sitter space, which mirrors the expanding universe we inhabit, remains less explored.
Our work begins by establishing the theoretical foundations of the WGC and its manifestations in standard quantum field theories in flat Minkowski space, in which the conjecture takes two distinct variations. The first stems from a black hole discharge perspective, and the other, known as the Repulsive Force Conjecture (RFC), stems from a particle physics perspective. While the two variations are distinct, they can, in fact, coalesce into one under certain circumstances. In the frame of this work, we shall discuss what is known as the electric WGC, which is simply the WGC in a theory that couples gravity with only one U(1) gauge symmetry. We shall see how, when observing this theory in Minkowski space, we obtain that the two formulations unite in the absence of scalar fields.
Subsequently, our focus shifts to the challenges and nuances introduced when extending the conjectures to de Sitter space. We begin by understanding in what domain in space our classical description is still valid. Once we understand this. we move on to derive the RFC in de-Sitter space, this way we have what to compare with already existing attempts to introduce the WGC to de-Sitter space. Once we have done this, we can ask ourselves what is the critical value of the cosmological constant that still allows the formation of bound states in de-Sitter space thus allowing us to put a bound on the cosmological constant. This will eventually lead to a new swampland constraint. Lastly, once having done all this work, we can finally address the research question of this work of whether the RFC and the WGC remain equivalent in de-Sitter space. To address this question, we shall independently revisit each side of this equivalence in the classical, non-relativistic domain, where we portray spacetime as a perturbation about flat space. Lastly, in the end, we will briefly cover why the question of whether the equivalence in de-Sitter still holds is not a trivial question.
We restate that this thesis is entirely contained in the classical, non-relativistic domain. In this domain, we shall derive the charge-to-mass ratio in de-Sitter space from a repulsive force perspective and from a black hole discharge perspective independently. We shall see that the two ratios disagree, indicating that perhaps the WGC-RFC equivalence does not hold in de-Sitter space. In addition, we also utilize the RF formulation and its connection to the cosmological constant in de-Sitter to show how it affects the ability of pure gravitational systems to form bound states. We use this to produce a bound on the cosmological constant that still enables the formation of bound states. We also extract a direct link between the gauge coupling constant of a spherically symmetric U(1) theory and the cutoff on its classical domain.