  Primordial perturbations in our universe are believed to have a quantum
origin, and can be described by the wavefunction of the universe (or
equivalently, cosmological correlators). It follows that these observables must
carry the imprint of the founding principle of quantum mechanics: unitary time
evolution. Indeed, it was recently discovered that unitarity implies an
infinite set of relations among tree-level wavefunction coefficients, dubbed
the Cosmological Optical Theorem. Here, we show that unitarity leads to a
systematic set of "Cosmological Cutting Rules" which constrain wavefunction
coefficients for any number of fields and to any loop order. These rules fix
the discontinuity of an n-loop diagram in terms of lower-loop diagrams and the
discontinuity of tree-level diagrams in terms of tree-level diagrams with fewer
external fields. Our results apply with remarkable generality, namely for
arbitrary interactions of fields of any mass and any spin with a Bunch-Davies
vacuum around a very general class of FLRW spacetimes. As an application, we
show how one-loop corrections in the Effective Field Theory of inflation are
fixed by tree-level calculations and discuss related perturbative unitarity
bounds. These findings greatly extend the potential of using unitarity to
bootstrap cosmological observables and to restrict the space of consistent
effective field theories on curved spacetimes.
