Scalar propagator for planar gravitational waves

TL;DR

This paper derives the massive scalar propagator in planar gravitational wave backgrounds, enabling analysis of quantum scalar fields and their interactions in such curved spacetime settings.

Contribution

It introduces a novel representation of the scalar propagator in gravitational wave backgrounds using deformed nonlocal distances and computes key quantum effects.

Findings

Energy-momentum tensor shows energy flow aligned with gravitational waves.

Effective action and scalar mass are unaffected by gravitational waves.

Energy density flow increases with scalar mass, wave amplitude, and frequency.

Abstract

We construct the massive scalar propagator for planar gravitational wave backgrounds propagating on Minkowski space. We represent the propagator in terms of the Bessel's function of suitably deformed nonlocal distance functions, the deformation being caused by gravitational waves. We calculate the propagator both for nonpolarized, for the plus ($+$) and cross ($\times$) polarized plane waves, as well as for more general planar waves both in $D$ space-time dimensions. The propagator is useful for studying interactions of scalar fields on planar gravitational wave backgrounds in the context of interacting quantum fields, in which renormalization plays a crucial role. As simple applications of the propagator we calculate the one-loop effective action, the scalar mass generated by the scalar self-interaction term and the one-loop energy-momentum tensor, all renormalized by using dimensional regularization and renormalization. While the effective action and scalar mass remain unaffected by gravitational waves, the energy-momentum tensor exhibits flow of energy density in the direction of gravitational waves which grows quadratically with the scalar field mass, gravitational wave amplitude and its frequency.