Searching for cosmological gravitational-wave backgrounds with third-generation detectors in the presence of an astrophysical foreground

The stochastic cosmological gravitational-wave background (CGWB) provides a direct window to study early universe phenomena and fundamental physics. With the proposed third-generation ground-based gravitational wave detectors, Einstein Telescope (ET) and Cosmic Explorer (CE), we might be able to detect evidence of a CGWB. However, to dig out these prime signals would be a difficult quest as the dominance of the astrophysical foreground from compact-binary coalescence (CBC) will mask this CGWB. In this paper, we study a subtraction-noise projection method, making it possible to reduce the residuals left after subtraction of the astrophysical foreground of CBCs, greatly improving our chances to detect a cosmological background. We carried out our analysis based on simulations of ET and CE and using posterior sampling for the parameter estimation of binary black-hole mergers. We demonstrate the sensitivity improvement of stochastic gravitational-wave searches and conclude that the ultimate sensitivity of these searches will not be limited by residuals left when subtracting the estimated BBH foreground, but by the fraction of the astrophysical foreground that cannot be detected even with third-generation instruments, or possibly by other signals not included in our analysis. We also resolve previous misconceptions of residual noise in the context of Gaussian parameter estimation.

Figure 1

Design sensitivities of current and future GW detectors.

Figure 2

Mass range for individual BBH mass used in our study.

Figure 3

Distribution of total mass $M$ and redshift $z$ of the 100 BBH signals used in our analysis. High-SNR signals are chosen for clearest possible demonstration of the projection method to mitigate the astrophysical foreground.

Figure 4

Simulated astrophysical foreground, subtraction residuals, and residual spectrum after projection for ET without instrument noise (except for the max-posterior parameter estimation).

Figure 5

ORF $\gamma (f)$ between Cosmic Explorer (CE) and Einstein Telescope (ET). The ORFs are shown over a logarithmic (top) and linear (bottom) frequency axis. Note that the ORF between different detectors of the ET triangle is constant with a value of about −0.38.

Figure 6

Optimal filter function $\tilde{Q}(f)$ between CE and ET plotted over a logarithmic (top) and linear (bottom) frequency axis. The optimal filters between detectors of the ET triangle are all identical.

Figure 7

Signal-to-noise ratio of a flat ${\mathrm{\Omega }}_{\mathrm{GW}}=2\times {10}^{-12}$ stochastic background. The curves are the SNRs accumulated from high to low frequencies. Total observation time is 1.3 years.

Figure 8

Plots of residual CSDs averaged over all ET detector pairs with BBH foreground (top, left), after best-fit subtraction (top, right), and after noise projection (bottom). The CPSDs are 1.3-year averages and also averaged over all detector pairs of the ET triangle with a total of ${10}^6$ injected BBHs. The astrophysical reference model (red curves) is only an approximation valid below about 100 Hz since it is predicted to fall more strongly above 100 Hz. The purple curve represents a CGWB with frequency independent ${\mathrm{\Omega }}_{\mathrm{GW}}={10}^{-15}$. The blue curves are the simulated CPSD measurements. The green curves are the predicted instrument noise. The orange curves show the CPSDs for simulations without instrument noise.