PhD project: Emergent matrix cosmology

Project description

The goal of this project will be to find a first-principles derivation of an early-universe paradigm from a non-perturbative description of String Theory, namely Matrix Theory. It is indeed well-known that matrix models can, in a suitable large-N limit, lead to the emergence of spacetime. However, how matrix degrees of freedom encode geometric information is something that needs to be better understood. This project will mostly focus on the method of applying the collective field formalism to gauged matrix models. Given some recent results regarding how one integrates out off-diagonal elements in this approach, one of the goals will be to compute the gauge-invariant target space entanglement entropy of these models in the collective field approach. Another would be examining different toy matrix models and their connection to quantum gravity in lower dimensions. Examining the vacuum structure of the collective field will lead to a direct connection between Matrix Cosmology and String Gas Cosmology, establishing why there is a dynamical compactification in this picture. Since it maintains a direct relationship with String Theory, and does not invoke arbitrary free parameters, it will provide unambiguous predictions. The phenomenological predictions of such a paradigm, with regards to its predictions for cosmological observables, shall also be explored in this project.

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