The predictive power of cosmic inflation hinges on the existence of a conserved quantity at very large scales, called the primordial curvature perturbation, which is therefore insensitive to the details of reheating and the physics of the hot big bang. Whether the classical spacetime symmetries responsible for this conservation law can enforce it at the quantum level is an old debate. Although this was never explicitly proven, cosmologists often assume that this freezing holds at all loop orders and that inflationary predictions can always be propagated to the radiation era, with primordial fluctuations playing the role of seeds for the large-scale structures that we observe in our Universe today. In this work, by consistently using the effective field theory of inflationary fluctuations, we explicitly prove for the first time that the renormalized one-loop power spectrum of the primordial curvature perturbation freezes exactly on scales larger than its sound horizon.

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• Inflation
• Large scale structure of the Universe
• Quantum fields in curved spacetime