  It is shown that phantom scalar models can be mapped into a mathematically
equivalent, modified $F(R)$ gravity, which turns out to be complex, in general.
Only for even scalar potentials is the ensuing modified gravity real. It is
also demonstrated that, even in this case, modified gravity becomes complex at
the region where the original phantom dark energy theory develops a Big Rip
singularity. A number of explicit examples are presented which show that these
two theories are not completely equivalent, from the physical viewpoint. This
basically owes to the fact that the physical metric in both theories differ in
a time-dependent conformal factor. As a result, an FRW accelerating solution,
or FRW instanton, in the scalar-tensor theory may look as a deccelerating FRW
solution, or a non-instantonic one, in the corresponding modified gravity
theory.
