Revisiting van Citter-Zernike correlations in the presence of primordial gravitational waves

TL;DR

This paper investigates how primordial gravitational waves affect the spatial coherence of electromagnetic signals from distant sources, showing that the resulting blurring constrains GW backgrounds but remains undetectable with current VLBI technology.

Contribution

It introduces a quantum field theory framework to analyze the impact of primordial GWs on electromagnetic coherence and quantifies the resulting blurring effect.

Findings

Primordial GWs cause a loss of spatial coherence in EM signals.

The induced incoherence is too weak for current VLBI detection.

Constraints on GW background amplitude are derived from coherence observations.

Abstract

In this paper, we develop a quantum field theory framework to describe the interaction between a gravitational wave (GW) background and an electromagnetic (EM) field emitted from a distant celestial source, such as a star. We demonstrate that a background of primordial gravitational waves (PGWs), as predicted by the inflationary scenario, induces a loss of spatial coherence in the EM field as it propagates over cosmological distances. This effect leads to the degradation of van Cittert-Zernike correlations, ultimately rendering them unobservable - a phenomenon referred to as blurring. Since spatial coherence is observed in very long baseline interferometry (VLBI) measurements of distant quasars, this places constraints on the amplitude of the PGW background. We quantitatively evaluate the blurring effect caused by PGWs in a two-mode squeezed state, which represents the standard quantum state predicted by the simplest inflationary models. However, due to the weak coupling between GWs and the EM field, we find that the induced incoherence is too small to be detected in current VLBI observations.