Universal relation between the variances of distortions of gravitational waves owing to gravitational lensing

Abstract

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.

7 pages, 2 figures, Published in ApJ Letters

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Cited by in corpus (6)

• Amplitude and phase fluctuations of gravitational waves magnified by strong gravitational lensing
• Weak lensing of gravitational waves in wave optics: Beyond the Born approximation
• Kramers-Kronig relation in gravitational lensing
• The Born approximation in wave optics gravitational lensing revisited
• New Consistency Relations between Averages and Variances of Weakly Lensed Signals of Gravitational Waves
• Consistency relations of amplitude and phase fluctuations of gravitational waves magnified by strong gravitational lensing