Non-perturbative over-production of axion-like-particles (ALPs) via derivative interaction

Axion like particles (ALPs) are quite generic in many scenarios for physics beyond the Standard Model, they are pseudoscalar Nambu-Goldstone bosons, and appear once any global $U(1)$ symmetry is broken spontaneously. The ALPs can gain mass from various non-perturbative quantum effects, such as anomalies or instantons. ALPs can couple to the matter sector incluidng a scalar condensate such as inflaton or moduli field via derivative interactions, which are suppressed by the axion {\it decay constant}, $f_\chi$ . Although weakly interacting, the ALPs can be produced abundantly from the coherent oscillations of a homogeneous condensate. In this paper we will study such a scenario where the ALPs can be produced abundantly, and in some cases can even overclose the Universe via odd and even dimensional operators, as long as $f_\chi/\Phi_{\rm I} \ll 1$, where $\Phi_{\rm I}$ denotes the initial amplitude of the coherent oscillations of the scalar condensate, $\phi$. We will briefly mention how such dangerous overproduction would affect dark matter and dark radiation abundances in the Universe.