http://arxiv.org/abs/2210.02062

Universe’s matter inhomogeneity gravitationally affects the propagation of gravitational waves (GWs), causing the lensing effect. Particularly, the weak lensing of GWs contains abundance of information about the small scale matter power spectrum and it has been studied within the range of the Born approximation. In this work, we investigate the validity of the Born approximation by accounting for the higher order terms in the gravitational potential $\Phi$. We first develop the formulation of the post-Born approximation, which is made by introducing a new variable. We then derive the expression of the magnitude and the phase of the amplification factor up to third order in $\Phi$ and compute the average and variance beyond the Born approximation. Our results suggest that the post-Born effect is indeed a few orders of magnitude smaller than the leading order contribution within almost all frequency ranges considered in this work except for the high frequency area $f\sim1000$ Hz, where the shot noise is dominant. Intriguingly, the number of necessary GW events for detecting the average, which originates purely from the post-Born effect, could become comparable or even smaller than the number required for detecting the variance, which appears at the level of the Born approximation. This indicates that the average is measurable with the same detection cost as the variance, even though it is only a few percent of the variance. On the other hand, we find that, even though the detection of the post-Born corrections to the variance would be possible in the case of the magnification, extracting the useful information to infer the shape of the matter power spectrum is still challenging even for the future generation GW detectors. This is due to the smallness of the post-Born effect and the difficulty of separating it from both the noise signal and the Born approximation effect.

Read this paper on arXiv…

M. Mizuno and T. Suyama
Thu, 6 Oct 22
31/77

Comments: 39 pages, 8 figures