Probing small-scale power spectrum with gravitational-wave diffractive lensing
摘要
We develop a novel way to probe subgalactic-scale matter distribution with diffractive lensing on gravitational waves. Five-year observations from Einstein Telescope and DECIGO are expected to probe k = 105 ∼ 108 Mpc−1 down to P (k) = 10−16 ∼ 10−14 Mpc3 level. These results can be interpreted in terms of primordial black holes in the range MPBH ≳ 10−3M⊙ down to fPBH = 10−6 level, or QCD axion minihalos in the range ma = 10−3 ∼ 10−12 eV. A key result of the paper is the approximate relation between the scale k and the gravitational wave frequency f, derived in an ensemble of ‘multi-lensing’ events. This relation enables direct measurement of the power spectrum at specific scales, with sensitivities characterized by model-independent kernels δP (k). Additionally, we delineate the statistical properties of ‘multi-lensing’ based on the ‘Fresnel number’ NF. When NF ≳