Bounding alternative theories of gravity with multiband GW observations

We study the constraints on alternative theories of gravity that can be determined by multiband observations of gravitational wave signals emitted from binary black hole coalescences. We focus on three types of General Relativity modifications induced by a generalized Brans-Dicke theory and two classes of quadratic gravity, Einstein-dilaton-Gauss-Bonnet and dynamical Chern-Simons. Considering a network of space- and ground-based detectors, supplied by a population of spinning binaries black holes, we show how the multiband analysis improves the existing bounds on the theory's parameters by several orders of magnitude, for both pre- and post-Newtonian deviations. Our results also show the fundamental role played by an interferometer in the frequency range between LISA and advanced detectors, in constraining possible deviations from General Relativity.