Mirror matter, mirror gravity and galactic rotational curves

We discuss astrophysical implications of the modified gravity model in which the two matter components, ordinary and dark, couple to separate gravitational fields that mix to each other through small mass terms. There are two spin-2 eigenstates: the massless graviton, which induces universal Newtonian attraction, and the massive one, which gives rise to the Yukawa-like potential which is repulsive between the ordinary and dark bodies. As a result for distances much smaller than the Yukawa radius r (m) the gravitation strength between the two types of matter becomes vanishing. If r (m) similar to 10 kpc, the typical size of a galaxy, there are interesting implications for the nature of dark matter. In particular, one can avoid the problem of the cusp that is typical for the cold dark matter halos. Interestingly, the flat shape of the rotational curves can be explained even in the case of the collisional and dissipative dark matter (as e.g. mirror matter), which cannot give the extended halos but instead must form galactic discs similarly to the visible matter. The observed rotational curves for the large, medium-size and dwarf galaxies can be nicely reproduced. We also briefly discuss possible implications for the direct search of dark matter.