Tensor Catalyzed Decoherence of Primordial Scalar Fluctuations

Abstract

We provide the first complete calculation of the leading contribution to the decoherence of primordial fluctuations in the scalar part of the metric fluctuations within simplest, single-clock, inflationary models, assuming decoherence comes from gravitational interactions with an environment made up of the other, unmeasured, short-wavelength scalar and tensor modes. We include the contributions from {\it all} of the contributing interactions at leading order in powers of $(H/M_p)^2$ and of the slow-roll parameter $\epsilon_1$. Unlike all extant calculations in the literature we find a result that is {\it not} slow-roll suppressed (and so is the same order of magnitude as tensor-mode decoherence). The difference arises because the dominant decoherence comes from interactions that involve {\it both} the tensor and scalar environments simultaneously (and so are missed when they are examined separately). We verify that the leading contributions to decoherence are UV finite (as they must be). We confirm that the interactions driving decoherence become time-local and Gaussian in the deep super-Hubble inflationary regime and show how this can be used to reliably compute the evolution of the purity in the late-time regime relevant for observations (where naive perturbation theory is known to break down). The same derivation shows explicitly why the effects that undermine perturbation theory for decoherence do not also undermine the basic inflationary prediction for the amplitude of primordial fluctuations (in agreement with general arguments).2