Cutting Cosmological Correlators

TL;DR

Unitarity fixes the analytic structure of the cosmological wavefunction, and the authors derive an infinite set of single-cut rules that generalize the Cosmological Optical Theorem (COT). The rules hold for fields with linear dispersion across general FLRW spacetimes, masses, spins, and derivative interactions, provided the Bunch-Davies vacuum is adopted. The authors verify the framework in nontrivial cases including conformally coupled and massive scalar exchanges, a four-graviton exchange, and a five-point function, and discuss connections to the Cosmological Cutting Rules and bootstrap programs. The results offer a powerful, general constraint on cosmological correlators with potential impact on cosmological collider phenomenology and holographic interpretations.

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.

Figures (4)

• Figure 1: Diagrammatic representation of the single-cut rules defined in \ref{['eq:Cut']} demonstrating the interpretation of the right-hand side as the cutting of an internal line in the diagram on the left-hand side. A cut line is pushed to the bounday, i.e. it is substituted by two external lines and a factor of the power spectrum. The discontinuity should be taken of each of the two resulting diagrams. The circles represent an arbitrary tree-level diagram with any number of internal lines.
• Figure 2: The diagram shows the $s$-channel for the interaction of 4 conformally coupled scalars exchanging a conformally coupled scalar. A similar diagram describes the massive exchange case.
• Figure 3: Diagram showing the s-channel for an interaction involving 4 gravitons exchanging a graviton.
• Figure 4: Diagram showing the geometry for the 5 point interaction which is being considered in \ref{['eq:flat5']}. There are other diagrams that involve permutations of the labeling of the momenta that must be considered so that the wavefunction coefficient is symmetric in the momenta.