The linearized theory of a relativistic plasma in a radiation backgrou
nd, proposed recently by Holcomb and Tajima, is extended for a more ge
neral background with the metric components being an arbitrary power f
unction of time (approximately t(n)). It is noted that the electric fi
eld falls off faster and the redshift of the electromagnetic radiation
frequency is also greater in a more rapidly expanding background univ
erse. The dispersion relation for the transverse vibration of the elec
tromagnetic field, however, appears to be independent of the parameter
n. The wave equation for the electric field is solved for a de Sitter
background also.