Timeless Quantum Mechanics and the Early Universe

Introduction.- Classical Diffeomorphism Invariance on the Worldline.- Quantum Diffeomorphism Invariance on the Worldline. The Relativistic Particle as an Archetypical Example.- Homogeneous Classical and Quantum Cosmology.- Weak-Coupling Expansion-. Quantum-Gravitational Effects in the Early Universe.- Conclusions and Outlook.- Appendix A Review of Gauge Systems and Constrained Dynamics.- Appendix B. The Traditional Born-Oppenheimer Approach to the Problem of Time.

Leonardo Chataignier completed his PhD degree in Theoretical Physics at the University of Cologne (Germany) with the highest distinction (summa cum laude) in 2021. His research focuses on quantum gravity and quantum cosmology, and more specifically on the investigation of the consequences of diffeomorphism invariance to the formalism of quantum mechanics. His PhD thesis presents a new method of relating quantum states to probabilities without an external or preferred time parameter, and of describing the quantum dynamics in a diffeomorphism-invariant way. This method may facilitate the construction and conceptual understanding of a fundamental theory of quantum gravity. Before his PhD work, Chataignier completed his Master's degree (MSc) in Theoretical Physics at Utrecht University (The Netherlands) with the highest distinction (cum laude) in 2017, and his Bachelor's degree (BSc) in Physics with a Certificate of Additional Studies in Mathematics at the Pontifical Catholic University of Rio de Janeiro (Brazil) in 2014, having received a number of "Prizes for Academic Merit'', a "Prize for Outstanding Undergraduate Research'', as well as a "Physics Challenge Scholarship'', which covered the tuition fees for the duration of his Bachelor's studies (2011-2014).