General Relativity & Quantum Cosmology

I discuss work in progress on the no-boundary state of the universe in quantum cosmology, emphasizing the key role played by the inclusion of an observer in obtaining a reasonable no-boundary state. For concreteness we focus on a 2d toy model, namely dS JT gravity. This model has avatars of important issues with the wavefunction of the universe in inflationary models. The issues are that the wavefunction predicts a small universe (whereas our universe is rather large), and that it is not normalizable. I show that the non-normalizability is resolved by promoting dS JT gravity to sine dilaton gravity, a type of UV completion of dS JT gravity of which I discuss the cosmological interpretation. I then argue that the issue of predicting a small universe (in this toy model) is resolved by including an observer in the theory. With the observer, the leading contribution is a bra-ket wormhole. The observer's no boundary state is a (maximally mixed) identity matrix, and thus prefers neither small nor large universes.

Local subsystems play a fundamental role in theoretical physics, but they are usually defined in terms of background spacetime structures, in particular a Lorentzian metric. In gravity there are no such structures and the metric becomes dynamical. I will argue that nevertheless subsystems can be constructed in relation to other degrees of freedom, subject to the requirement that those variables reside within the subsystem itself. In operational terms an observer located within the system should be able to determine its edge by taking measurements within that region only. Within the context of classical field theory, I will demonstrate that this guarantees that the observables describing the system constitute a closed Poisson algebra. I'll discuss some examples, explain how surface charges generating subsystem symmetries, including the Bekenstein-Hawking area entropy, are incorporated, and make some remarks about how this can be extended to a fully quantum treatment within the framework of deformation quantization.