Dark radiation measurements could reveal when the universe first heated up

Light axions produced during reheating contribute to dark radiation, quantified as ΔN_eff, through two distinct channels: direct inflaton decay and inflaton annihilation. These scale oppositely with reheating temperature — decay falls as T_rh^{-2} while annihilation grows as T_rh^{4/3} — so analyses that include only one channel miss the crossing between them. A shift-symmetric EFT organizes both contributions into a two-dimensional map of Wilson coefficients, translating current and future ΔN_eff measurements into simultaneous lower and upper bounds on the reheating temperature.