In-in formalism, pseudo-instantons and rethinking quantum cosmology

TL;DR

This paper explores the in-in formalism in quantum cosmology, revealing pseudo-instantons that enable tunneling between vacua, challenging traditional in-out perspectives and suggesting a need to rethink quantum cosmological models.

Contribution

It demonstrates that stationary phase approximation behaves differently in the in-in formalism, leading to the discovery of pseudo-instantons that affect tunneling phenomena in cosmology.

Findings

Pseudo-instantons enable tunneling between vacua in infinite volume.

Stationary phase approximation differs significantly in in-in path integrals.

Reevaluation of in-out formalism notions in the context of quantum cosmology.

Abstract

Unlike flat space quantum field theories that focus on scattering amplitudes, the main observables in quantum cosmology are correlation functions. The systematic way of calculating correlators is called in-in formalism, which requires only a single asymptotic region, i.e. past infinity. The rules in perturbation theory and the path integral measure are very different for in-in and in-out formalisms, and thus the results which are standard in one approach may not necessarily hold in the other one. We show that stationary phase approximation works completely different for a scalar in-in path integral. Hence, in a cosmological background there are solutions, pseudo-instantons, that allow tunneling between locally stable vacua even in infinite volume, which is counterintuitive from an in-out perspective. We argue that various familiar notions of in-out formalism must be reexamined in the in-in formalism, which might have important consequences for quantum cosmology.