2026/06/03 by S. Shajidul Haque, Bret Underwood
Physics and Astronomy · #gr-qc #astro-ph.CO #hep-th
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. Within this landscape we show that decoherence models that "classicalize" -- in the sense of admitting a regular, positive-definite Glauber-Sudarshan P-function -- must actively inject momentum into the system, exceeding that of the vacuum. The enhanced momentum sources the decaying mode of the curvature perturbation, backreacting on the Newtonian potential and radiation-era geometry. While this mode decays away fast enough to preserve the temporal coherence of the CMB acoustic peaks, requiring the potential to remain within linear perturbation theory places a model-independent bound on the momentum variance generated by any model of decoherence. This bound is definitively violated by decohered thermal states with more than 14 e-folds of inflation, while a strong dependence on the number of e-folds restricts amplitude-basis decoherence to fewer than roughly 64 e-folds of inflation in order to stay in the linear regime. Altogether, we present a unifying framework for evaluating the quantum-to-classical transition of the early universe.