General Relativity & Quantum Cosmology

In this talk, we analyze detector operators that measure energy to the power ∆-2 at null infinity in Einstein gravity. These operators transform as conformal primaries on the celestial sphere and provide a natural basis for describing energy-flux observables in scattering processes. Using the collinear factorization of scattering amplitudes, we derive the universal leading structure of the operator product expansion (OPE). A key consequence of our analysis is the precise identification of the ∆=2 detector, the number operator. Exploiting the fact that soft charges generate symmetries of the S-matrix, we demonstrate that the number of particles is entirely determined by the product of two supertranslation currents. This work establishes a direct link between detector observables and the soft sector of celestial holography. Analogous conclusions hold for Yang–Mills theory. 

We explicitly construct the density matrix associated to the vacuum state of a large spherically symmetric causal diamond in four-dimensional asymptotically flat gravity. We achieve this using the soft effective action, which characterizes the low-energy gravitational degrees of freedom that arise in the long-distance limit of the Einstein-Hilbert action and consists of both the soft graviton mode and the Goldstone mode arising from the spontaneous breaking of supertranslation symmetry. Once we have the density matrix, we straightforwardly compute the mean and variance of the modular Hamiltonian and in particular show that the variance obeys an area law.