Superfluid vacuum theory and deformed dispersion relations

Using the logarithmic superfluid model of physical vacuum, one can formulate a quantum theory, which successfully recovers Einstein's theory of relativity in low-momenta limit, but otherwise has different foundations and predictions. We present an analytical example of the dispersion relation and argue that it should have a Landau "roton" form which ensures the suppression of dissipative fluctuations. We show that at small momenta, a dispersion relation becomes relativistic with small deformations, such that a photon acquires effective mass, but a much more complex picture arises at large momenta.
Comment: 3 pages, 1 figure, based on the talk given at the Tenth Alexander Friedmann International Seminar on Gravitation and Cosmology, Saint Petersburg, 24-28 June 2019