General Relativity & Quantum Cosmology

Motivated by recent advances in "non-Lorentzian" physics, I will revisit the light-cone formulation of QFT, which has played a central role in the quantization of gauge theories. Much of its success can be traced to the presence of an underlying non-relativistic (Galilean) structure within the light-cone Poincaré algebra. I will show that light-cone Minkowski space belongs to a broader class of non-Lorentzian geometries, whose isometry algebra accommodates several interesting kinematical subalgebras—particularly of the Galilean and Carrollian types. These kinematical Lie algebras encode the symmetry transformations that govern spacetime kinematics and the evolution of physical systems. Finally, I will discuss certain aspects of light-cone field theories, emphasizing their connection to the hypersurface deformation algebra associated with Carrollian geometries, as well as their possible implications.

The good books on GR agree on certain aspects of the theory that we could consider to be its “core” features. Beyond the core, however, we do not know exactly what GR should allow or not allow physically. For example, should we consider spacetimes with closed causal loops as part of physical GR or not? Are spacetimes with certain types of boundaries or singularities part of GR?  Most people expect that the answer to these sorts of questions will be answered by quantum gravity when we have it.  We can start to address them within different quantum gravity approaches even at their current partial state of their development. Within the framework of the path integral for quantum gravity and a Feynmanian heuristic for the recovery of the classical approximation, I will sketch out how answers may arise. I will use the example of causal set quantum gravity but I suggest that the ideas are applicable to other path integral approaches.

The first part of the talk will briefly discuss the tasks that need to be accomplished in order to formulate such open quantum models in the context of quantum gravity, as well as the challenges involved. As a first step in this direction, a QFT model in the context of linearised gravity is presented, which is formulated in Ashtekar-Barbero variables and then Fock-quantised with a special choice of so-called geometrical clocks as a reference frame. The corresponding master equation and its renormalisation are discussed. Inspired by this QFT model, the second part of the talk presents an application of a quantum mechanical toy model in the context of neutrino oscillations and compares it with existing phenomenological models.

Models for gravitationally induced decoherence can be formulated within the framework of open quantum systems, in which gravity is chosen as the environment and quantised together with the system under consideration. The effective dynamics of the system under the influence of the environment are encoded in the so-called master equation. Existing phenomenological models often take the Lindblad equation as the starting point for the master equation, while from the perspective of quantum gravity approaches, an underlying microscopic model from which a field-theoretical master equation can be derived seems to be the more accessible approach, which also makes it possible to establish a connection between microscopic and phenomenological models.