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

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.