Würzburg Seminar on Quantum Field Theory and Gravity

We obtain solutions of the Wheeler-DeWitt equation with positive cosmological constant for a closed universe in the large-volume limit. We argue that this space of solutions provides a complete basis for the Hilbert space of quantum gravity in an asymptotically deSitter spacetime. Our solutions take the form of a universal phase factor multiplied by distinct diffeomorphism invariant functionals, with simple Weyl transformation properties, obeying the same Ward identities as a CFT partition function. The Euclidean vacuum corresponds to a specific choice of such a functional but other choices are equally valid. Each functional can be thought of as specifying a “theory” and the space of solutions is like “theory space”. We describe another basis for Hilbert space where all states are represented as excitations of the vacuum that have a specific constrained structure. This gives the finite GN generalization of the basis proposed by Higuchi in terms of group averaging. We also discuss the inner product structure in the Hilbert space. We apply our formalism to understand cosmological correlators & find a version of principle of holography of information: cosmological correlators in an arbitrarily small region suffice to completely specify the state.