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The background of primordial gravitational waves (PGWs) predicted by theinflationary scenario induce incoherence of the electromagnetic fieldpropagating over cosmological distances. We propose a new schema to constrainthe underlying inflationary parameters, in particular the tensor-to-scalarratio r, based on angular size-redshift \theta-z measurement accomplished byvery long baseline interferometry (VLBI) surveys. VLBI observations rely on thevan-Citter Zernike theorem, which expresses the coherence length in terms ofits wavelength and angular size, i.e., d_coh < \lambda/\theta. In this study,we show that the interaction of the radio signal (involved in VLBI) with PGWs,along the propagation from a source located at redshift z_* to the Earth, leadsto the blurring of the visibility. The blurring effect is evaluated for thehighly-squeezed PGW, where it turns out that in order not to ruin thevisibility, the projected baseline of the interferometer must be smaller than\xi_sq(z), which is inversely proportional to the the tensor-to-scalar ratiothrough \xi_sq \propto r^{-1/2}. Hence, VLBI observations based on interferencepattern lead to a constraint on r imposed by the fact that \xi_sq(z) is greaterthan d_coh of the emitted radiation. In order to evaluate the constraint, weuse a sample of compact radio quasars observed in VLBI and located at redshiftrange 0.46<z<2.73. We obtain a stringent upper-bound on the tensor-to-scalarratio, r<2.10^{-6}, far beyond present constraints on this parameter. Furtherissues and caveats that potentially affect the results are reviewed. Inparticular, the possible effect of quantum-to-classical transition of PGWs isdiscussed. Ultimately, the background of primordial tensor perturbations may bemore constrained with the help of the high-precision VLBI measurement ofangular size-redshift of more distant sources.

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