Stability of singularity-resolving effective theories of gravity
A fundamental question in physics is whether spacetime singularities really exist or whether they are mere limitations of our incomplete theories. To answer the question without a full understanding of quantum gravity, a modest approach is to try finding healthy semi-classical theories that could represent effective bottom-up descriptions of quantum gravity and which admit non-singular spacetime solutions. I will present a few proposals, but the focus will be on the Cuscuton, an incompressible scalar field that modifies general relativity dynamics without introducing new degrees of freedom. To connect with the previous talk by Prof. Ghazal Geshnizjani, I will then discuss how linear perturbation theory can be used to assess the stability and soundness of the theory. I will end with a few words about non-linear stability.