Group velocity of weak waves on spatially flat nonstationary background

A group velocity of a planar wave packet is an established notion for a wave propagation on a spatially flat and stationary background. In the general relativity, the spacetime is usually not spatially flat, which makes it difficult to define a planar wave packet. But within the theory of cosmological perturbations, the spacetime can be considered to be spatially flat and nonstationary. Therefore it is possible to study the propagation of the planar wave packet also in this nonstationary case. However, it turns out to be difficult to distinguish a wave packet “propagating in one direction” from a general superposition with opposite direction. One possible approach to this problem is presented. It utilises a limit behaviour for small wavelengths, and it gives the group velocity as a Taylor series.