Universal Constraints on Axions from Inflation
  We consider the presence of an axion like particle, $\sigma$, with a generic
$CP$ violating axial coupling of the form $ (\alpha \, \sigma/f) F \tilde{F}$,
where $F_{\mu\nu}$ is the gauge field strength of a generic abelian $U(1)$
gauge group, not necessarily associated with the standard electromagnetism, and
$f$ is the decay constant of the axion. It has previously been demonstrated
that if the axion is identified with the inflaton, such an interaction can lead
to measurable cosmological signatures (non-Gaussian modifications of the
curvature perturbation spectrum) depending on the parameter $\xi= \alpha
\dot{\sigma}/ (f H)$. In the present paper we will show that the generation of
curvature perturbation at horizon crossing due to the axial coupling has a
universal form and remains unmodified in terms of the $\xi$ parameter even if
the axion, $\sigma$, is not identified with the inflaton. As a consequence, it
does not appear to be possible to generate CMB tensor perturbations through
this mechanism, larger than the vacuum ones, without violating the
observational constraints unless we combine this mechanism with a curvaton or
if the $\sigma$ field becomes heavy and decays during inflation. Even in this
last case there are non-trivial constraints coming from the slow-roll evolution
of the curvature perturbation on super horizon scales which should be taken
into account. We also comment on implications for inflationary models where
axions play an important role as, for example, models of natural inflation
where more than one axion are included and models where the curvaton is an
axion.
