Variational dynamics in open spacetimes

TL;DR

This paper explores how non-zero surface terms at spatial infinity influence scalar field dynamics in open FLRW spacetimes, revealing their significance at classical and quantum levels, especially with supercurvature perturbations.

Contribution

It demonstrates that surface terms, often neglected, can significantly affect scalar field dynamics in open spacetimes, a novel insight in quantum field theory in curved backgrounds.

Findings

Surface terms can impact classical field configurations.

Surface contributions are relevant for quantum field dynamics.

Supercurvature perturbations amplify surface term effects.

Abstract

We study the effect of non-vanishing surface terms at spatial infinity on the dynamics of a scalar field in an open FLRW spacetime. Starting from the path-integral formulation of quantum field theory we argue that classical physics is described by field configurations which extremize the action functional in the space of field configurations for which the variation of the action is well defined. Since these field configurations are not required to vanish outside a bounded domain, there is generally a non-vanishing contribution of a surface term to the variation of the action. We then investigate whether this surface term has an effect on the dynamics of the action-extremizing field configurations. This question appears to be surprisingly nontrivial in the case of the open FLRW geometry, since surface terms tend to grow as fast as volume terms in the infinite volume limit. We find that surface terms can be important for the dynamics of the field at a classical and at a quantum level, when there are supercurvature perturbations.