  A number of diagrammatic "cutting rules" have recently been developed for the
wavefunction of the Universe which determines cosmological correlation
functions. These leverage perturbative unitarity to relate particular
"discontinuities" in Feynman-Witten diagrams (with cosmological boundary
conditions) to simpler diagrams, in much the same way that the Cutkosky rules
relate different scattering amplitudes. In this work, we make use of a further
causality condition to derive new cutting rules for Feynman-Witten diagrams.
These lead to the cosmological analogue of Feynman's tree theorem for
amplitudes, which can be used to systematically expand any loop diagram in
terms of (momentum integrals of) tree-level diagrams. As an application of
these new rules, we show that certain singularities in the wavefunction cannot
appear in equal-time correlators due to a cancellation between "real" and
"virtual" contributions that closely parallels the KLN theorem. Finally, when
combined with the Bunch-Davies condition that certain unphysical singularities
are absent, these cutting rules completely determine any tree-level exchange
diagram in terms of simpler contact diagrams. Altogether, these results remove
the need to ever perform nested time integrals when computing cosmological
correlators.
