  The initial conditions of our universe appear to us in the form of a
classical probability distribution that we probe with cosmological
observations. In the current leading paradigm, this probability distribution
arises from a quantum mechanical wavefunction of the universe. Here we ask what
the imprint of quantum mechanics is on the late time observables. We show that
the requirement of unitary time evolution, colloquially the conservation of
probabilities, fixes the analytic structure of the wavefunction and of all the
cosmological correlators it encodes. In particular, we derive in perturbation
theory an infinite set of single-cut rules that generalize the Cosmological
Optical Theorem and relate a certain discontinuity of any tree-level $n$-point
function to that of lower-point functions. Our rules are closely related to,
but distinct from the recently derived Cosmological Cutting Rules. They follow
from the choice of the Bunch-Davies vacuum and a simple property of the
(bulk-to-bulk) propagator and are astoundingly general: we prove that they are
valid for fields with a linear dispersion relation and any mass, any integer
spin and arbitrary local interactions with any number of derivatives. They also
apply to general FLRW spacetimes admitting a Bunch-Davies vacuum, including de
Sitter, slow-roll inflation, power-law cosmologies and even resonant
oscillations in axion monodromy. We verify the single-cut rules in a number of
non-trivial examples, including four massless scalars exchanging a massive
scalar, as relevant for cosmological collider physics, four gravitons
exchanging a graviton, and a scalar five-point function.
