  The Bootstrap approach to calculating cosmological correlators relies on a
well motivated ansatz. It is typical in the literature to assume that
correlators are rational functions as this greatly increases our constraining
power. However, this has only previously been demonstrated for some specific
theories. In this paper we find a set of assumptions which we prove are
sufficient to ensure that the wavefunction coefficients are rational. As a
corollary of this we generalise the manifestly local test to higher dimensions.
This result greatly reduces the allowed space of functions that wavefunction
coefficients can take in both the Effective Field Theory of Inflation and Pure
Gravity models and is thus a key ingredient in the Cosmological Bootstrap
program.
