  We explore some of the cosmological implications of the recent classical
nonlocal generalization of Einstein's theory of gravitation in which
nonlocality is due to the gravitational memory of past events. In the Newtonian
regime of this theory, the nonlocal character of gravity simulates dark matter
in spiral galaxies and clusters of galaxies. However, dark matter is considered
indispensable as well for structure formation in standard models of cosmology.
Can nonlocal gravity solve the problem of structure formation without recourse
to dark matter? Here we make a beginning in this direction by extending
nonlocal gravity in the Newtonian regime to the cosmological domain. The
nonlocal analog of the Zel'dovich solution is formulated and the consequences
of the resulting nonlocal Zel'dovich model are investigated in detail.
