Cosmological Cutting Rules

TL;DR

This paper establishes Cosmological Cutting Rules derived from unitarity principles, providing a systematic way to relate loop-level wavefunction coefficients to lower-order diagrams in cosmology, applicable to a broad class of models and spacetimes.

Contribution

It introduces a general set of Cosmological Cutting Rules that constrain wavefunction coefficients at any loop order, extending unitarity-based methods to cosmological settings.

Findings

Cutting rules relate loop diagrams to lower-loop diagrams and tree-level diagrams.

One-loop corrections in inflation EFT are determined by tree-level calculations.

Results apply broadly to fields of any mass, spin, and general FLRW spacetimes.

Abstract

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.