Amplitude and Phase Fluctuations for Gravitational Waves Propagating through Inhomogeneous Mass Distribution in the Universe

Abstract

When a gravitational wave (GW) from a distant source propagates through the universe, its amplitude and phase change due to gravitational lensing by the inhomogeneous mass distribution. We derive the amplitude and phase fluctuations, and calculate these variances in the limit of a weak gravitational field of density perturbation. If the scale of the perturbation is smaller than the Fresnel scale $\sim 100pc(f/mHz{)}^{-1/2}$ ($f$ is the GW frequency), the GW is not magnified due to the diffraction effect. The rms amplitude fluctuation is $1-10$ for $f>10^{-10}$ Hz, but it is reduced less than 5% for a very low frequency of $f<10^{-12}$ Hz. The rms phase fluctuation in the chirp signal is $\sim 10^{-3}$ radian at LISA frequency band ($10^{-5}-10^{-1}$ Hz). Measurements of these fluctuations will provide information about the matter power spectrum on the Fresnel scale $\sim 100$ pc.

6 pages, 6 figures, refferences added, accepted for publication in ApJ

References in corpus (8)

• Using gravitational-wave standard sirens
• Wave Effects in Gravitational Lensing of Gravitational Waves from Chirping Binaries
• Detecting the stochastic gravitational wave background using pulsar timing
• LISA observations of rapidly spinning massive black hole binary systems
• Finding the Electromagnetic Counterparts of Cosmological Standard Sirens
• Scattering of gravitational radiation: second order moments of the wave amplitude
• Scattering of Gravitational Waves by the Weak Gravitational Fields of Lens Objects
• Effects of finite arm-length of LISA on analysis of gravitational waves from MBH binaries

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