Leading gravitational dressing of operators and states in de Sitter space

Abstract

We describe construction of gravitationally dressed observables in de Sitter (dS) space, to leading non-trivial order in Newton's constant. We show that for an underlying field theory observable to be "gravitationally dressable," it must be dS invariant. If it satisfies this condition, its gravitational dressing can be constructed in terms of certain Green functions, by solving the condition that the dressed observable commute with the constraints. We provide a construction of the Green functions relevant for dressing observables lying on a time-symmetric slice. A simple example of a dS invariant observable is an operator creating a two-particle state of scalars. In the large mass limit, the particles are shown to be antipodally located, and the dressing of this operator (or corresponding state) can be explicitly constructed. Its behavior is diagnosed by certain correlators involving this state, and we check explicitly that these correlators then reproduce a linearized version of the Schwarzschild-dS solution. The underlying dS-invariant observables may be thought of as relational, and we argue can be generalized to include systems with properties of observers, which then could be likewise gravitationally dressed. We also briefly describe how such dressed observables can be related to alpha vacua, and discuss other questions regarding a more complete construction and role of such operators.