All-Loop Renormalization and the Phase of the de Sitter Wavefunction

Alexander Farren; Ciaran McCulloch; Enrico Pajer; Xi Tong

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arXiv · 2603.08794

All-Loop Renormalization and the Phase of the de Sitter Wavefunction

Alexander Farren·Ciaran McCulloch·Enrico Pajer·Xi Tong

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Abstract

Cosmological observables of the primordial universe are encoded in the late-time field-theoretic wavefunction. For shift-symmetric scalars in de Sitter, a good approximation for many inflationary models, the wavefunction must be purely real at tree-level. This property is violated by a quantum anomaly in the process of renormalization. As a result, we show that the imaginary part of the wavefunction is fixed by its dependence on the renormalization scale to all loop orders in perturbation theory. This follows from unitarity, locality, dilation isometry and a Bunch-Davies state. The compact relation we uncover for the wavefunction implies an infinite set of relations among correlators of massless fields and their conjugate momenta, which we exemplify at one-loop order.

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Alexander Farren, Ciaran McCulloch, Enrico Pajer, Xi Tong. 2026-03-09. All-Loop Renormalization and the Phase of the de Sitter Wavefunction. https://arxiv.org/abs/2603.08794

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