  It is widely known that the primordial curvature perturbation $\zeta$ has
several universal properties in the infrared (IR) such as the soft theorem,
which is also known as the consistency relation, and the conservation in time.
They are valid in rather general single clock models of inflation. It has been
argued that these universal properties are deeply related to the large gauge
transformations in inflationary spacetime. However, the invariance under the
large gauge transformations is not sufficient to show these IR properties. In
this paper, we show that the locality condition is crucial to show the
consistency relation and the conservation of $\zeta$. This argument also can
apply to an interacting system with the inflaton and heavy fields which have
arbitrary integer spins, including higher spin fields, which may be motivated
from string theory. We will also show that the locality condition guarantees
the cancellation of the IR divergences in a certain class of variables whose
correlation functions resemble cosmologically observable quantities.
