Geometric Dark Matter

Abstract

The dark matter, needed for various phenomena ranging from flat rotation curves to structure formation, seems to be not only neutral and long-living but also highly secluded from the ordinary matter. Here we show that, metric-affine gravity, which involves metric tensor and affine connection as two independent fields, dynamically reduces, in its minimal form, to the usual gravity plus a massive vector field. The vector, which interacts with only the quarks, leptons and gravity, is neutral and long-living (longer than the age of the Universe) when its mass range is $9.4\mathrm{MeV}<M_Y<28.4\mathrm{MeV}$. Its scattering cross section from nucleons, which is some 60 orders of magnitude below the current bounds, is too small to facilitate direct detection of the dark matter. This property provides an explanation for whys and hows of dark matter searches. We show that due to its geometrical origin the $Y_{\mu }$ does not couple to scalars and gauge bosons. It couples only to fermions. This very feature of the $Y_{\mu }$ makes it fundamentally different than all the other vector dark matter candidates in the literature. The geometrical dark matter we present is minimal and self-consistent not only theoretically but also astrophysically in that its feebly interacting nature is all that is needed for its longevity.

arXiv comment7 pages, 2 figures. v2: restored a missing factor, added a reference; v3: added a reference, minor improvements in text, journal version

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