  Scalar polarization modes of gravitational waves, which are often introduced
in the context of the viable extension of gravity, have been actively searched.
However, couplings of the scalar modes to the matter are strongly constrained
by the fifth-force experiments. Thus, the amplitude of scalar polarization in
the observed gravitational-wave signal must be significantly suppressed
compared to that of the tensor modes. Here, we discuss the implications of the
experiments in the solar system on the detectability of scalar modes in
gravitational waves from compact binary coalescences, taking into account the
whole processes from the generation to the observation of gravitational waves.
We first claim that the energy carried by the scalar modes at the generation
is, at most, that of the tensor modes from the observed phase evolution of the
inspiral gravitational waves. Next, we formulate general gravitational-wave
propagation and point out that the energy flux hardly changes through
propagation as long as the background changes slowly compared to the wavelength
of the propagating waves. Finally, we show that the possible magnitude of
scalar polarization modes detected by the ground-based gravitational-wave
telescopes is already severely constrained by the existing gravity tests in the
solar system.
