On the anisotropies of the cosmological gravitational-wave background from pulsar timing array observations

Significant evidence for a stochastic gravitational-wave background has recently been reported by several Pulsar Timing Array observations. These studies have shown that, in addition to astrophysical explanations based on supermassive black hole binaries (SMBHBs), cosmological origins are considered equally important sources for these signals. To further explore these cosmological sources, in this study, we discuss the anisotropies in the cosmological gravitational wave background (CGWB) in a model-independent way. Taking the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) 15-year dataset as a benchmark, we estimate the angular power spectra of the CGWB and their cross-correlations with cosmic microwave background (CMB) fluctuations and weak gravitational lensing. We find that the NANOGrav 15-year data implies suppressed Sachs-Wolf (SW) effects in the CGBW spectrum, leading to a marginally negative cross-correlation with the CMB at large scales. This procedure is applicable to signals introduced by different early universe processes and is potentially useful for identifying unique features about anisotropies of CGWB from future space-based interferometers and astrometric measurements.