Frequency Modulation of Gravitational Waves by Ultralight Scalar Dark Matter

The oscillating pressure of the ultralight scalar dark matter (DM) can induce the oscillation of the local gravitational potential. Similar to the time-dependent frequency shift for the pulse signals of pulsars, the oscillation of the local gravitational potential can induce a time-dependent frequency shift (or frequency modulation) for quasi-monochromatic gravitational wave (GW) signals from galactic white dwarf (WD) binaries. To make this effects detectable, we suppose that some galactic WD binaries are located in the DM clumps/subhalos where the energy density of DM is about eight orders of magnitude higher than that at the position of the Earth. Turn to the fisher information matrix, we find that the amplified GW frequency modulation induced by the ultralight scalar DM with mass $m=1.67\times10^{-23}-4.31\times10^{-23}[{\rm eV}/c^2]$ can be detected by LISA.