  A Smarandache multi-space is a union of $n$ different spaces equipped with
some different structures for an integer $n\geq 2$, which can be both used for
discrete or connected spaces, particularly for geometries and spacetimes in
theoretical physics. This is the 4th part of multi-spaces considering
applications of multi-spaces to theoretical physics, including the relativity
theory, the M-theory and the cosmology. Multi-space models for $p$-branes and
cosmos are constructed and some questions in cosmology are clarified by
multi-spaces.
