Normal Modes for Massive Spin 1 Equation in Robertson–Walker Space-Time

The general scheme of the massive spin-1 equation in curved space-time with associated conserved current is considered. A properly covariant scalar product between solutions of the spin-1 equation is defined in a standard way by means of the conservation of the current. The scheme is specialized to the Robertson–Walker space-time where solutions of the spin-1 equation have been previously determined. There results, in case of flat Robertson–Walker space-time, the automatic ortho-normalization property of the solutions, that therefore represent a set of normal modes.