Within the Berezhiani-Khoury superfluid dark matter framework, the equation of state belongs to a one-parameter family with polytropic index Gamma. We show that Gamma = 3 is the only value for which the phonon-mediated force law is independent of the dark matter density profile. The acoustic metric conformal factor Omega = rho/cₛ is proportional to rho^ ( (3-Gamma) /2), which is spatially constant if and only if Gamma = 3. When Omega varies, it introduces density-dependent corrections to the phonon transmission that break the universality of the radial acceleration relation. Correspondence: simd01@icloud. com
Simon Dillworth (Fri,) studied this question.