Scalar polarization window in gravitational-wave signals

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.