1pm - 2pm: Cosmological Correlators: Unitarity and Renormalization

Cosmological observables of the primordial universe are encoded in the late-time field-theoretic wavefunction. I begin with a pedagogical review of the constraints on the wavefunction imposed by fundamental principles such as unitarity, locality, and causality. I then show that for shift-symmetric scalars in de Sitter—an excellent approximation for many inflationary models—the wavefunction is purely real at tree level. This property is violated by a quantum anomaly that arises from ultraviolet divergences and the subsequent process of renormalization.

I discuss the main renormalization procedures employed in cosmology, namely dimensional regularization, mass-and-dimension regularization, and the recently introduced eta-regulators, emphasizing the crucial differences with flat-spacetime quantum field theory. I then show that, to all loop orders in perturbation theory, the imaginary part of the renormalized wavefunction is fixed by its dependence on the renormalization scale. This result follows from unitarity, locality, dilation symmetry, and the assumption of a Bunch–Davies vacuum. The compact relation I present for the wavefunction implies an infinite set of constraints among correlators of massless fields and their conjugate momenta, which I illustrate explicitly at one-loop order.