  We investigate four-dimensional effective theories which are obtained by
dimensional reduction of multidimensional cosmological models with factorizable
geometry and consider the interaction between conformal excitations of the
internal space (geometrical moduli excitations) and Abelian gauge fields. It is
assumed that the internal space background can be stabilized by minima of an
effective potential. The conformal excitations over such a background have the
form of massive scalar fields (gravitational excitons) propagating in the
external spacetime. We discuss cosmological and astrophysical implications of
the interaction between gravexcitons and four-dimensional photons as well as
constraints arising on multidimensional models of the type considered in our
paper. In particular, we show that due to the experimental bounds on the
variation of the fine structure constant, gravexcitons should decay before
nucleosynthesis starts. For a successful nucleosynthesis the masses of the
decaying gravexcitons should be m>10^4 GeV. Furthermore, we discuss the
possible contribution of gravexcitons to UHECR. It is shown that, at energies
of about 10^{20}eV, the decay length of gravexcitons with masses m>10^4 GeV is
very small, but that for m <10^2 GeV it becomes much larger than the
Greisen-Zatsepin-Kuzmin cut-off distance. Finally, we investigate the
possibility for gravexciton-photon oscillations in strong magnetic fields of
astrophysical objects. The corresponding estimates indicate that even the high
magnetic field strengths of magnetars are not sufficient for an efficient and
copious production of gravexcitons.
