Universal relation between the variances of distortions of gravitational
  waves owing to gravitational lensing
  Gravitational waves from the distant sources are gravitationally lensed
during their propagation through the intervening matter inhomogeneities before
arriving at detectors. It has been proposed in the literature that the variance
of the lensed waveform can be used to extract information of the matter power
spectrum at very small scales and of low-mass dark halos. In this paper, we
show that the variance of the amplitude fluctuation and that of the phase
fluctuation of the lensed waveform obey a simple relation irrespective of the
shape of the matter power spectrum. We study conditions under which this
relation can be violated and discuss some potential applications of the
relation. This relation may be used to confirm the robustness of claimed
observations of gravitational lensing of gravitational waves and the subsequent
reconstruction of the matter power spectrum.
