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Recent observations of gravitational waves from binary black holes andneutron stars allow us to probe the strong and dynamical field regime ofgravity. On the other hand, a collective signal from many individual,unresolved sources results in what is known as a stochastic background. We hereconsider probing gravity with such a background from stellar-mass binary blackhole mergers. We adopt a simple power-law spectrum and carry out a parameterestimation study with a network of current and future ground-based detectors byincluding both general relativistic and beyond general relativistic variables.For a network of second-generation detectors, we find that one can placemeaningful bounds on the deviation parameter in the gravitational-waveamplitude if it enters at a sufficiently negative post-Newtonian order.However, such future bounds from a stochastic background are weaker thanexisting bounds from individual sources, such as GW150914 and GW151226. We alsofind that systematic errors due to mismodeling of the spectrum is much smallerthan statistical errors, which justifies our use of the power-law model.Regarding a network of third-generation detectors, we find that the bounds onthe deviation parameter from statistical errors improve upon thesecond-generation case, though systematic errors now dominate the error budgetand thus one needs to use a more realistic spectrum model. We conclude thatindividual sources seem to be more powerful in probing general relativity thanthe astrophysical stochastic background.

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