  If a light axion is present during inflation and becomes part of dark matter
afterwards, its quantum fluctuations contribute to dark matter isocurvature. In
this article, we introduce a whole new suite of cosmological observables for
axion isocurvature, which could help test the presence of axions, as well as
its coupling to the inflaton and other heavy spectator fields during inflation
such as the radial mode of the Peccei-Quinn field. They include correlated
clock signals in the curvature and isocurvature spectra, and mixed
cosmological-collider non-Gaussianities involving both curvature and
isocurvature fluctuations with shapes and running unconstrained by the current
data analyses. Taking into account of the existing strong constraints on axion
isocurvature fluctuations from the CMB, these novel signals could still be
sizable and potentially observable. In some models, the signals, if observed,
could even help us significantly narrow down the range of the inflationary
Hubble scale, a crucial parameter difficult to be determined in general,
independent of the tensor mode.
