Abstract
Gravitational waves (GWs) from cosmological double neutron star binaries ($\mathrm{NS}+\mathrm{NS}$) 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 $\mathrm{NS}+\mathrm{NSs}$, the residual foreground would be below the detection limit ${\ensuremath{\Omega}}_{\mathrm{GW},\mathrm{lim}}\ensuremath{\sim}{10}^{\ensuremath{-}16}$ realized with the Big Bang Observer/Deci-hertz Interferometer Gravitational Wave Observatory by correlation analysis.
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