Exploring the quantum gravity regime

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All of the matter we know of in the universe is composed of atoms glued together by various interactions. The matter moves in space and time as actors move on a stage. But then what is the stage composed of? What are the atoms of space and time? Einstein showed that space and time can be unified in a single concept, space-time. He also realized that the geometric features of this space-time can be understood as a manifestation of the gravitational force, so that the stage and the actors interact with one another. Finding a consistent theoretical description of such atoms of space-time is one of the greatest challenges of theoretical physics. My research program has as its aims: 1- improving the theoretical description of the atoms of space-time suggested by the loop quantum gravity (LQG) framework, 2- probing the physics of such atoms of space-time. One key feature in my program is to focus on 3d space-times, i.e., those with only 2 spatial dimensions. Gravity then becomes topological which means that there are no local degrees of freedom, hence no gravitational waves. This can be viewed as a solvable toy model, getting rid of some difficult aspects of the 4d physical theory while retaining its salient features. I intend in particular to test my different theoretical proposals before extending them to the realistic 4d case. Black holes are purely gravitational objects, also existing in 3d. Their nature and fate (will they evaporate?), which depend on their fundamental quantum nature, mesmerizes both expert researchers and an eager public. My research will advance significantly the understanding of the quantum nature of these objects in the 3d case, using the LQG formalism and technical tools I have introduced. For example, I will precisely calculate whether such black hole quantum state could tunnel to a white hole quantum state, probing effectively the concept of Planck stars introduced recently by Rovelli et al. There is unfortunately little hope of devising experiments to probe the quantum gravity regime since it would amount to recreating the conditions at the origin of the Universe. Interestingly, 3d gravity being topological shares many features with models studied in condensed matter and even in quantum information theory in order to build quantum computers. I am proposing to use these similarities to identify features of 3d quantum gravity in condensed matter models to mimic quantum gravity effects in some experiments that could in principle be implemented in a lab. This proposal would create a new research area “analogue quantum gravity”, which would circumvent some of the difficulties to have access to experimental facts about quantum gravity. Quantum gravity provides great means for outreach and for attracting STEM students. As a subfield of mathematical physics, it provides excellent training for students who will be able to work in the private or public sectors, improving Canadian competitiveness.