  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.
