  We study the dynamics of Abelian gauge fields invariant under transverse
diffeomorphisms (TDiff) in cosmological contexts. We show that in the geometric
optics approximation, very much as for Diff invariant theories, the
corresponding massless gauge bosons propagate along null geodesics and particle
number is conserved. In addition, the polarization vectors are orthogonal to
the propagation direction and the physical (transverse projection) polarization
is parallel transported along the geodesics. We also consider TDiff invariant
Dirac spinors, study the coupling to the gauge fields and analyze the
conditions in order to avoid violations of Einstein's Equivalence Principle.
The contributions to the energy-momentum tensor of the gauge field are also
analyzed. We find that, in general, the breaking of Diff invariance makes the
electric and magnetic parts of the vector field to gravitate in a different
way. In the sub-Hubble regime we recover the standard radiation-like behaviour
of the energy density, however in the super-Hubble regime the behaviour is
totally different to the Diff case, thus opening up a wide range of
possibilities for cosmological model building. In particular, possible effects
on the evolution of large-scale primordial magnetic fields are discussed.
