We assume that dark energy and dark matter filling up the whole cosmic space behave as a special superfluid, here named “superfluid quantum space.” We analyze the relationship between intrinsic pressure of SQS (dark energy's repulsive force) and gravity, described as an inflow of dark energy into massive particles, causing a negative pressure gradient around massive bodies. Since no superfluid has exact zero viscosity, we analyze the consequences of SQS’s viscosity on light propagation, and we show that a static Universe could be possible, by solving a modified Navier-Stokes equation. Indeed, Hubble’s law may actually refer to tired light, though described as energy loss due to SQS’s nonzero viscosity instead of Compton scattering, bypassing known historical problems concerning tired light. We see that SQS’s viscosity may also account for the Pioneer anomaly. Our evaluation gives a magnitude of the anomalous acceleration aP = −HΛc = −8.785°10−10 ms−2. Here, HΛ is the Hubble parameter loaded by the cosmological constant Λ. Furthermore, the vorticity equation stemming from the modified Navier-Stokes equation gives a solution for flat profile of the orbital speed of spiral galaxies and discloses what one might call a breathing of galaxies due to energy exchange between the galactic vortex and dark energy.
Part of the book: Trends in Modern Cosmology