  Cosmological correlators capture the spatial fluctuations imprinted during
the earliest episodes of the universe. While they are generally very
non-trivial functions of the kinematic variables, they are known to arise as
solutions to special sets of differential equations. In this work we use this
fact to uncover the underlying tame structure for such correlators and argue
that they admit a well-defined notion of complexity. In particular, building
upon the recently proposed kinematic flow algorithm, we show that tree-level
cosmological correlators of a generic scalar field theory in an FLRW spacetime
belong to the class of Pfaffian functions. Since Pfaffian functions admit a
notion of complexity, we can give explicit bounds on the topological and
computational complexity of cosmological correlators. We conclude with some
speculative comments on the general tame structures capturing all cosmological
correlators and the connection between complexity and the emergence of time.
