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.
