Constraining alternative theories of gravity using GW150914 and GW151226

The recently reported gravitational wave events GW150914 and GW151226 caused by the mergers of binary black holes [Abbott et al., Phys. Rev. Lett. 116, 221101 (2016); Phys. Rev. Lett. 116, 241103 (2016); Phys. Rev. X 6, 041015] provide a formidable way to set constraints on alternative metric theories of gravity in the strong field regime. In this paper, we develop an approach where an arbitrary theory of gravity can be parametrized by an effective coupling G_eff and an effective gravitational potential Φ (r ). The standard Newtonian limit of general relativity is recovered as soon as G_eff→G_N and Φ (r )→Φ_N. The upper bound on the graviton mass and the gravitational interaction length, reported by the LIGO-VIRGO Collaboration, can be directly recast in terms of the parameters of the theory that allows an analysis where the gravitational wave frequency modulation sets constraints on the range of possible alternative models of gravity. Numerical results based on published parameters for the binary black hole mergers are also reported. The comparison of the observed phases of GW150914 and GW151226 with the modulated phase in alternative theories of gravity does not give reasonable constraints due to the large uncertainties in the estimated parameters for the coalescing black holes. In addition to these general considerations, we obtain limits for the frequency dependence of the α parameter in scalar tensor theories of gravity.