An EFT Map of Axion Dark Radiation from Reheating

Abstract

Light, weakly coupled sectors can retain information about the cosmological background in which they are produced. We study light axions produced during reheating and their contribution to dark radiation, $\Delta N_{\rm eff}$. We develop a shift-symmetric EFT in which an inflaton-dependent axion kinetic term systematically organizes the leading production channels. The same kinetic function generates both direct inflaton decay and inflaton annihilation from the oscillating inflaton background. Direct decay is described by an invisible inflaton branching fraction, while annihilation is a genuinely reheating-sensitive source controlled by a coherent combination of Wilson coefficients. We derive the contribution to $\Delta N_{\rm eff}$ from both channels and show that they scale oppositely with the reheating temperature: the decay contribution falls as $T_{\rm rh}^{-2}$, whereas the annihilation contribution grows approximately as $T_{\rm rh}^{4/3}$. Their crossing is missed by treatments that keep only one production channel. We translate current and projected $\Delta N_{\rm eff}$ sensitivities into constraints on the Wilson coefficients of the kinetic function, obtaining a two-dimensional EFT map of axion dark radiation from reheating. This map can imply both lower and upper bounds on the reheating temperature, showing that light axion relics can turn dark radiation measurements into constraints on reheating.