Demagnified gravitational waves from cosmological double neutron stars and gravitational wave foreground cleaning around 1 Hz

Gravitational waves (GWs) from cosmological double neutron star binaries (NS+NS) can be significantly demagnified by the strong gravitational lensing effect, and the proposed future missions such as the Big Bang Observer or Deci-hertz Interferometer Gravitational Wave Observatory might miss some of the demagnified GW signals below a detection threshold. The undetectable binaries would form a GW foreground, which might hamper detection of a very weak primordial GW signal. We discuss the outlook of this potential problem, using a simple model based on the singular isothermal sphere lens profile. Fortunately, it is expected that, for a presumable merger rate of NS+NSs, the residual foreground would be below the detection limit ₆ₖ, ₋₈₌10^-16 realized with the Big Bang Observer/Deci-hertz Interferometer Gravitational Wave Observatory by correlation analysis.