Constraining tensor-to-scalar ratio based on VLBI observations: PGWs induced-incoherence approach

In this study, we show that the background of primordial gravitational waves (PGWs) predicted by the inflationary scenario induce a decrease of the spatial coherence length of an electromagnetic field propagating over cosmological distances, leading the van Citter-Zernike correlations to eventually be unobservable, an affect called as blurring. Since this spatial correlation is actually observed in VLBI measurements of distant quasars, it imposes a constraint on the level of the primordial gravitational waves background. In this paper, we precisely evaluate this blurring effect by considering the primordial gravitational waves background to be in the so-called two-mode squeezed state, which is the standard quantum state predicted by the simplest scenario of inflation. We then exploit a sample of compact radio quasars located at redshift range $0.46\leq z \leq 2.73$ observed by very long baseline interferometry (VLBI) means. These quasars constitute a standard ruler and the angular size-distance $\theta-z$ relation is determined thanks to the measurement of their spatial coherence. These spatial coherence observations set an upper limit on the squeezing parameters of the PGWs background, which turns into an upper limit for the tensor-to-scalar ratio $\text{r}_{k_0}$. One finds $\text{r}_{k_0} < 10^{-7}$, five orders of magnitude better than present constraints on this parameter with the CMB. This result is nevertheless compatible with the possible detection of a cosmic background by the pulsar timing array measurement. Further issues and caveats that potentially affect the results are reviewed. In particular, the possible effect of quantum-to-classical transition of PGWs is discussed. Ultimately, we promote the idea of using high-precision VLBI measurement of angular size-redshift of distant sources as a new possible way of constraining the background of primordial tensor perturbations.
Comment: 61 pages, 7 figures, submitted to JCAP