Can machine learning improve the detectability and disentanglement of the gravitational-wave background?

Gravitational waves from compact binary coalescences and from early Universe processes are expected to form a gravitational-wave background. We employ a custom deep learning multi-scale multi-headed autoencoder architecture to isolate gravitational-wave background from detector noise, followed by a Markov chain Monte Carlo inference stage to separate the astrophysical and cosmological components. Analyzing $108$-day mock datasets representative of the first period of the fourth LIGO-Virgo-KAGRA observing run, we show that we can detect with high confidence --- $\log_{10}$ noise Bayes factor larger than 3 --- a compact binary coalescence gravitational-wave background with an amplitude of $4.3^{+0.5}_{-0.4}\times10^{-9}$ at $f_{\rm ref}=25\,\mathrm{Hz}$, which is a factor $\sim5$ higher than the amplitude expected from compact binary sources. We also show that we can isolate a cosmological -- assumed flat spectrum -- gravitational-wave background as weak as $9.7^{+2.5}_{-2.4} \times 10^{-10}$ from the expected compact binary coalescence gravitational-wave background within simulated Gaussian noise mimicking the LIGO detectors sensitivity achieved in the fourth observing run. In blind-test comparisons with the standard \texttt{pygwb} pipeline, we show that our method achieves more accurate amplitude and spectral-index recovery and enables the separation of astrophysical and cosmological background components.