Cutting Cosmological Correlators

TL;DR

This paper explores how quantum mechanics influences late-time cosmological observables by deriving general single-cut rules that relate cosmological correlators through unitarity, applicable across various fields, spins, and cosmological models.

Contribution

It introduces a set of general single-cut rules that extend the Cosmological Optical Theorem, applicable to a wide range of fields, spins, and cosmological backgrounds, based on unitarity and the Bunch-Davies vacuum.

Findings

Derived infinite set of single-cut rules for cosmological correlators.

Proved rules' validity for diverse fields and cosmologies.

Verified rules through multiple non-trivial examples.

Abstract

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.