Single-Field Inflation Fixes CMB Phase Coherence Solely via Observed Primordial Spectrum

The paper demonstrates that phase coherence, long viewed as a variable signature across different inflationary models, is instead locked by the measured primordial power spectrum alone. Because the comoving curvature perturbation remains constant outside the Hubble horizon, any differences in reheating temperature or duration wash out by recombination. This holds for any single-field slow-roll scenario without additional assumptions about the potential shape.

Standard treatments assumed higher-scale inflation would imprint stronger coherence through longer superhorizon evolution, yet the conservation law erases that dependence. The result follows directly from the separate-universe approach and the observed near-scale-invariant spectrum, without needing explicit mode-by-mode calculations. It therefore applies uniformly across the entire viable range of inflationary energies.

If confirmed, the finding removes one proposed observational discriminator between high- and low-scale inflation, shifting focus to tensor modes or non-Gaussianity. Future CMB experiments measuring peak sharpness to sub-percent precision could test the prediction, but only after foreground cleaning and lensing reconstruction reach the required accuracy.

The analysis rests on linear perturbation theory and the absence of entropy perturbations; any detection of isocurvature modes would reopen the question.