Estimation of the Stochastic Gravitational Wave Background from binary mergers

The ground-based International Gravitational-Wave Observatory Network (IGWN), including LIGO, Virgo, and KAGRA, has detected gravitational waves (GWs) from Compact Binary Coalescence (CBC) sources in galaxies up to 8 Gigaparsecs away, corresponding to a redshift slightly greater than 1. More distant sources, too faint for individual detection, are expected to form a detectable Stochastic Gravitational Wave Background (SGWB). While stringent upper limits on SGWB strength as a function of frequency in units of cosmological closure density of the universe, Ω_GW(f), have been made through IGWN, there has been no observed detection of SGWB. A preliminary detection of SGWB, announced on June 28, 2023, suggests the possibility of a signal from supermassive black hole mergers. However, the astrophysical background from all CBC sources in the LIGO frequency band remains undetected. Early implications for SGWB from first observation of stellar-mass Binary Black Hole (BBH) mergers and recent models from advanced LIGO and VIRGO data have provided estimates of CBC merger rate, which suggest that we are close to detecting SGWB. The estimates come from complex simulations of many individual events and numerical evaluation on an analytical expression for SGWB. We reproduce these estimates by using advanced models based on data from LIGO and Virgo to refine these estimates and study the degree to which they agree with each other, and the extent to which the results depend on uncertainties in the merger rate as a function of mass and redshift distributions of the sources. Our analysis constrains parameters of SGWB and decodes how this background evolves with respect to key astrophysical factors. By integrating state-of-the-art theoretical models, we aim to enhance the precision of SGWB estimates and move closer to its detection, thereby aiding in long-term goals of detecting SGWB with IGWN.