Gravitational-wave (GW) detections of binary neutron star coalescences play a crucial role to constrain the microscopic interaction of matter at ultrahigh density. Similarly, if boson stars exist in the universe, their coalescence can be used to constrain the fundamental coupling constants of a scalar field theory. We develop the first coherent waveform model for the inspiral of boson stars with quartic interactions. The waveform includes coherently spin-induced quadrupolar and tidal-deformability contributions in terms of the masses and spins of the binary and of a single coupling constant of the theory. We show that future instruments, such as the Einstein Telescope and the Laser Interferometer Space Antenna, can provide strong complementary bounds on bosonic self-interactions while the constraining power of current detectors is marginal.
