  The well known (3+1) decomposition of Thorne and Macdonald is invoked to
write down the Einstein-Maxwell equations generalised to (d+1) dimensions and
also to formulate the plasma equations in a flat FRW like spacetime in higher
dimensions (HD). Assuming an equation of state for the background metric we
find solutions as also dispersion relations in different regimes of the
universe in a unified manner both for magnetised(un) cold plasma. We find that
for a free photon in expanding background we get maximum redshift in 4D
spacetime, while for a particular dimension it is so in pre recombination era.
Further wave propagation in magnetised plasma is possible for a restricted
frequency range only, depending on the number of dimensions. Relevant to point
out that unlike the special relativistic result this allowed range evolves with
time. Interestingly the dielectric constant of the plasma media remains
constant, not sharing the expansion of the background, which generalises a
similar 4D result of Holcomb-Tajima in radiation background to the case of
higher dimensions with cosmic matter obeying an equation of state . Further,
analogous to the flat space static case we observe the phenomenon of Faraday
rotation in higher dimensional case also.
