The nature of dark matter

The observed strong dark-to-luminous matter coupling [F. Donato, et al., astro-ph/0403206, Mon. Not. R. Astron. Soc., submitted for publication; G. Gentile, et al., Mon. Not. R. Astron. Soc. 351 (2004) 903; D.T.F. Weldrake, et al., Mon. Not. R. Astron. Soc. 340 (2003) 12; W.J.G. de Blok, A. Bosma, Astron. Astrophys. 385 (2002) 816; O. Gerhard, et al., Astrophys. J. 121 (2001) 1936; A. Borriello, et al., Mon. Not. R. Astron. Soc. 341 (2003) 1109] suggests the existence of a some functional relation between visible and DM sources which leads to biased Einstein equations. We show that such a bias appears in the case when the topological structure of the actual Universe at very large distances does not match properly that of the Friedman space. We introduce a bias operator ρDM=Bˆρvis and show that the simple bias function b=1/(4πr0r2)θ(r−rmax) (the kernel of Bˆ) allows to account for all the variety of observed DM halos in astrophysical systems. In galaxies such a bias forms the cored DM distribution with the radius RC∼Ropt (which explains the recently observed strong correlation between RC and Ropt [F. Donato, et al., astro-ph/0403206, Mon. Not. R. Astron. Soc., submitted for publication]), while for a point source it produces the logarithmic correction to the Newton's potential (which explains the observed flat rotation curves in spirals). Finally, we show that in the theory suggested the galaxy formation process leads to a specific variation with time of all interaction constants and, in particular, of the fine structure constant.