  It is widely accepted that the Everett's (or "many-worlds") interpretation of
quantum mechanics is the only one which is appropriate for quantum cosmology
because no environment may exist for Universe as a whole. We discuss, in the
framework of the Everett's interpretation, the (quasi-) classical stage of
evolution of the Universe when there coexist "classically incompatible"
configurations of matter, or classical alternative realities ("alternatives"
for short). In the framework of the Everett's interpretation the semiclassical
gravity (where the gravitational field is classical and the non-gravitational
fields are quantum) is more natural than theories including quantizing
gravitational field. It is shown that the semiclassical (at least on the
astrophysical and cosmological scales) Everett-type gravity leads to the
observational effect known as the effect of dark matter. Instead of assuming
special forms of matter (weakly interacting with the known matter), the role of
the dark matter is played in this case by the matter of the usual kind which
however belongs to those alternative realities (Everett's worlds) which remain
{\guillemotleft}invisible{\guillemotright}, i.e. not perceived with the help of
non-gravitational fields.
