  Our understanding of quantum field theory rests largely on explicit and
controlled calculations in perturbation theory. Because of this, much recent
effort has been devoted to improve our grasp of perturbative techniques on
cosmological spacetimes. While scattering amplitudes in flat space at tree
level are obtained from simple algebraic operations, things are harder for
cosmological observables. Indeed, computing cosmological correlation functions
or the associated wavefunction coefficients requires evaluating a growing
number of nested time integrals already at tree level, which is computationally
challenging. Here, we present a new "differential" representation of the
cosmological wavefunction in de Sitter spacetime that obviates this problem for
a large class of phenomenologically relevant theories. Given any tree-level
Feynman-Witten diagram, we give simple algebraic rules to write down a seed
function and a differential operator that transforms it into the desired
wavefunction coefficient for any scale-invariant, parity-invariant theory of
massless scalars and gravitons with general boost-breaking interactions. In
particular, this applies to large classes of phenomenologically relevant
theories such as those described by the effective field theory of inflation or
solid inflation. Trading nested bulk time integrals for derivatives on boundary
kinematical data provides a great computational advantage, especially for
processes involving many vertices.
