Towards phenomenology from string theory

The fundamental forces of nature are gravity, explained by the theory of general relativity due to Einstein, and electromagnetic and nuclear forces, captured by quantum mechanics, when describing for instance atoms made of electrons and nucleus. It turns out to be incredibly difficult to unify these forces and theories into one common framework, that would for example describe the early days of our universe, right after the big bang, when it was filled with elementary particles. Interestingly, string theory is one of the rare candidates for such a fundamental theory. But it remains very difficult to connect it precisely to the world that we observe. For instance, string theory describes well universes that have a different shape than ours, or contain different particles. My research thus consists in trying to improve the connection of string theory to our world, or equivalently to understand whether it is possible to do so. In more details, my research project has three principal aims. The first one has to do with the actual shape of our universe: it has been observed to be expanding and accelerating, and is thus called a "de Sitter" universe. I will then determine conditions for having such a de Sitter universe described by string theory. The second aim goes the other way round: some other theories called supergravities admit such de Sitter universes, so the question becomes whether one can relate these theories, or even obtain them, from string theory. My goal is then to establish such a relation. Finally, the third part of my project aims at studying a subset of the particles usually obtained when starting from string theory, namely those similar to the Higgs boson. Achieving these three goals would be a non- trivial step towards connecting string theory to the world as we observe it.

It is an observed fact that not only our universe is expanding, but it does so at an accelerated rate. The energy responsible for this acceleration is not understood: it looks like nothing we know of, and is for this reason dubbed "dark energy". This acceleration and energy can be rephrased in terms of a certain geometry of our universe spacetime, called a de Sitter spacetime. In this project, we have tried to obtain such de Sitter spacetimes, starting from string theory. String theory is a candidate to be a fundamental theory describing nature. As such, it should provide an explanation to this mysterious dark energy. For this reason, we searched and found new kinds of solutions with de Sitter spacetimes, in a theory very close to string theory, called supergravity. The dark energy then corresponds to some ingredients present in extra dimensions allowed by the theory. We also studied some of the properties of these new solutions, namely their stability, which says how long such a universe would live. In previously found de Sitter solutions, they were not living long enough for being realistic, but we improved this situation in the project with these new solutions. It is notoriously difficult to find solutions with a de Sitter spacetime, mimicking our universe in accelerated expansion, from string theory. Recently some conjectures were made which state that such solutions do not exist, at least in some parts of string theory. In the project, we could prove in some framework these conjectures and make them precise, showing that they hold some truth. In string theory, many constructions aim at giving a realistic 4-dimensional physics model that describe our world. Most of those make use of massive objects called D-branes and orientifolds. These objects, as any massive object in general relativity, curve spacetime. In this project we determined for the first time the way they curve spacetime when some of the space dimensions are compact, for instance when having extra dimensions that are circles. This is a common situation in string theory inspired models. We then made use of this new information to study the propagation of 4-dimensional gravitational waves in presence of such massive objects and extra dimensions, and in order to compare this to future observations.