Homogeneous and Isotropic Linearized Gravity as a Caldeira--Leggett System

Abstract

We show that the homogeneous and isotropic sector of linearized gravity coupled to arbitrary additional degrees of freedom takes the Caldeira-Leggett form, provided their action contains no metric time derivatives at second order in perturbations. These additional degrees of freedom constitute the model's harmonic reservoir. Eliminating them yields a generalized Langevin equation for the metric perturbation, with their influence condensed in the reservoir's spectral density. This equivalence also yields a natural setting for reduced quantization of the perturbation and stochastic gravitational dynamics. We analyze the resulting dynamics with Laplace methods, extending results presented in other open-system settings.