Abstract
In the Newtonian limit of general relativity a force acting on a test mass in a central gravitational field is conventionally defined by the attractive Newtonian gravity (inverse square) term plus a small repulsive cosmological force, which is proportional to the slow acceleration of the universe expansion. In this paper we considered the cosmological-force correction due to fast quantum oscillations of the universe scale factor as a potential solution of the cosmological constant problem. These fast fluctuations of the cosmological scale factor violate Lorentz invariance at the Planck scale, and they induce strong changes to the current sign and magnitude of the average cosmological force, thus making it one of the potential probable causes for the modification of Newtonian dynamics in galaxy-scale systems. The modified cosmological force may be responsible for the recently discovered “cosmic-clock” behavior of disk galaxies in the low-redshift universe. The obtained results have strong implications for astroparticle physics since they demonstrate that typical galaxy rotation curves may be obtained without (or almost without) dark-matter particles.
Highlights
The discrepancy between visible masses in galaxies and galaxy clusters and their dynamics predicted by the application of Newton’s laws was first noticed by Fritz Zwicky almost a hundred years ago [1]
Newtonian dynamics of visible matter is typically attributed to a spherical dark-matter halo [2,6], 3
The difference between the measured rotation curve and the rotation curve calculated based on constant density, its mass distribution would be: the Newtonian dynamics of visible matter is typically attributed to a spherical dark-matter halo [2,6], which is assumed to exist around virtually every galaxy
Summary
The discrepancy between visible masses in galaxies and galaxy clusters and their dynamics predicted by the application of Newton’s laws was first noticed by Fritz Zwicky almost a hundred years ago [1]. The recently discovered “cosmic-clock” behavior [7] of disk galaxies in the low-redshift universe further underlines this discrepancy It appears that despite spanning a factor of 30 in size and velocity (from small irregular dwarf galaxies to the largest spirals) the galaxies behave as “clocks”, rotating roughly once in a billion years at the very outskirts of their discs. While this behavior strongly contradicts conventional Newtonian dynamics in the absence of dark-matter halos, it would require a very special fine tuning of the dark-matter halos around each galaxy. As we will try to demonstrate below, quite unexpectedly, a solution to this old problem may come from considerations of a Lorentz invariance violation at the Planck scale
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