The power of SKA to Constrain cosmological gravitational-wave backgrounds below the astrophysical foreground noise

The inspirals of supermaissive black hole binaries provide a convinced gravitational wave background in the nHz band, serving as the fiducial model of the recent gravitational wave signal reported by the PTA experiments. The uncertainties of the number of binaries contributing to each frequency bin introduce a foreground noise in the nHz and $\mu$Hz bands against the observation of the underlying gravitational wave backgrounds of the cosmological origin. In this work, we investigate a new method to constrain the cosmological gravitational wave strength under the astrophysical foreground. The energy density fluctuations from cosmological gravitational-wave sources can generally trigger the formation of compact subhalos of dark matter, and the upcoming Square Kilometer Array has the ability to constrain the abundance of the subhalos at the $\mathcal{O}(1)$ level. The cosmological gravitational wave energy spectra from various sources are expected to be constrained several orders of magnitude below the astrophysical foreground, providing more strict constraints on the parameter spaces of corresponding new physics models.