We investigate how a spatially modulated real scalar background Formula: see text can modify phonon propagation in the context of Superfluid dark matter (SFDM). Using a simple toy model with quartic condensate and coupling Formula: see text, we derive the local equation of state and the effective sound velocity Formula: see text. For Formula: see text, modulation tends to increase the effective mass of the condensate and make the medium less rigid, suppressing Formula: see text up to a “dust-like” regime, Formula: see text. We implement this modulation for the background scalar field by imposing rational profiles, through Padé radial profiles, and show the corresponding variation of Formula: see text for different Formula: see text, discussing implications for the structure of SFDM cores and the possible formation of inhomogeneous regions of dark matter.
Francesco Lottatori (Thu,) studied this question.