A Landscape of Cosmological Decoherence

Current observations constrain primordial perturbations to be adiabatic, approximately Gaussian, and nearly-scale invariant. However, a generic mixed state satisfying these constraints has additional unconstrained degrees of freedom, which can be parameterized by the purity of the state and its momentum variance. This allowable parameter space reveals a unified geometric landscape of mixed states, allowing us to map and relate distinct models of decoherence and their respective pointer bases. Crossing the threshold of a regular, positive-definite Glauber-Sudarshan $P$-function requires the environment to actively inject momentum into the system, rather than suppress it. This enhanced momentum variance dynamically sources the decaying mode of the gravitational potential in the radiation era. While the decaying mode vanishes fast enough to preserve the temporal coherence of the Cosmic Microwave Background, its initial amplitude places severe theoretical constraints on decoherence models to avoid gravitational non-linearities. These non-linearity bounds definitively rule out decohered thermal states, while long-wavelength divergences restrict amplitude-diagonal decoherence models to fewer than 70 $e$-folds of inflation. Altogether, we present a unifying framework for evaluating the quantum-to-classical transition of the early universe.