Freezing-in the Axiverse

The presence of multiple light axions in the infrared is a generic feature of many ultraviolet (UV) scenarios. In many cases the number of axions ${\cal N}$ is ${\cal O}(10-100)$ or more. Even in the scenario where these axions interact very weakly with the Standard Model (SM), the presence of ${\cal N}$ light axions poses a challenge to the stringent constraint on the number of relativistic degrees of freedom $N_{\rm eff}$. In order to remain agnostic about the UV, we adopt an effective field theory (EFT) approach, and parametrize the interactions of ${\cal N}$ axions with the SM to quantify the contribution to $N_{\rm eff}$. We consider operators up to dimension six, uncovering one previously-unconsidered charge radius operator, and pay particular attention to the flavor structure of the axion-SM fermion couplings and consider EFTs based on anarchy, textures, and minimal flavor violation. For various choices of such EFTs, we identify the discovery space for current and future cosmic microwave background surveys, including the Simons Observatory and CMB-HD. We show this discovery space depends sensitively on the flavor structure and exhibits a rich interplay with terrestrial and astrophysical probes.