Physical implications of extended teleparallel geometry

Research Project, 2025 –

Einstein's theory for gravity, general relativity, has been very successful in passing experimental tests. However, it is a classical theory, meaning that it does not involve quantum mechanics, which makes it very different from the theories for the other forces in nature. In order to understand the physics of the early universe or inside a black hole, where quantum mechanics becomes relevant, it needs to be extended. The overall purpose of this project is to analyse such extensions with the goal of understanding them better. The concrete objectives are (O1) to derive the effective field/particle spectrum in four dimensions, (O2) to calculate the speed and polarisation modes of gravitational waves, and (O3) to calculate quantities related to energy and entropy in gravity.

The theoretical framework for the project is extended geometry in its teleparallel formulation. The main metheodology that will be adopted in this proposal is perturbation theory, which can be applied to achieve both (O1) and (O2). In order to get a more robust answer to (O1), perturbation theory will be complemented by using Hamiltonian analysis through the Dirac-Bergmann algorithm of counting degrees of freedom. The Hamiltonian analysis can further be used to give an answer to (O3).