Constraining Modified Theories of Gravity with Gravitational-Wave Stochastic Backgrounds

The direct discovery of gravitational waves has finally opened a new observational window on our Universe, suggesting that the population of coalescing binary black holes is larger than previously expected. These sources produce an unresolved background of gravitational waves, potentially observable by ground-based interferometers. In this Letter we investigate how modified theories of gravity, modeled using the parametrized post-Einsteinian formalism, affect the expected signal, and analyze the detectability of the resulting stochastic background by current and future ground-based interferometers. We find the constraints that Advanced LIGO would be able to set on modified theories, showing that they may significantly improve the current bounds obtained from astrophysical observations of binary pulsars.