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

All-Loop Renormalization and the Phase of the de Sitter Wavefunction
Alexander Farren, Ciaran McCulloch, Enrico Pajer, Xi Tong
arXiv:2603.08794v1 Announce Type: cross
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.arXiv:2603.08794v1 Announce Type: cross
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.