  The first principles analysis of the radiation by an arbitrary source in a
flat Friedmann-Robertson-Walker space-time is presented. The obtained
analytical solution explicitly shows that the cosmological redshift is not of
kinematic origin and that the source and the observer may be regarded as being
at rest with respect to eachother at all times. At the same time the effect of
the time-variation of the metric on the propagation of light appears to be
underestimated in the standard cosmology. The cosmological redshift caused by
the linear time-variation of the metric turns out to be an exponential rather
than linear function of the well-defined spatial distance and the apparent
brightness of the source contains an even stronger exponential decay factor.
