Parameter Estimation for Tests of General Relativity with the Astrophysical Stochastic Gravitational Wave Background

Recent observations of gravitational waves from binary black holes and neutron stars allow us to probe the strong and dynamical field regime of gravity. On the other hand, a collective signal from many individual, unresolved sources results in what is known as a stochastic background. We here consider probing gravity with such a background from stellar-mass binary black hole mergers. We adopt a simple power-law spectrum and carry out a parameter estimation study with a network of current and future ground-based detectors by including both general relativistic and beyond general relativistic variables. For a network of second-generation detectors, we find that one can place meaningful bounds on the deviation parameter in the gravitational-wave amplitude if it enters at a sufficiently negative post-Newtonian order. However, such future bounds from a stochastic background are weaker than existing bounds from individual sources, such as GW150914 and GW151226. We also find that systematic errors due to mismodeling of the spectrum is much smaller than statistical errors, which justifies our use of the power-law model. Regarding a network of third-generation detectors, we find that the bounds on the deviation parameter from statistical errors improve upon the second-generation case, though systematic errors now dominate the error budget and thus one needs to use a more realistic spectrum model. We conclude that individual sources seem to be more powerful in probing general relativity than the astrophysical stochastic background.