I will discuss positivity bounds on EFT coefficients in theories where boosts are spontaneously broken. The well-known S-matrix argument from the Lorentz invariant scenario does not straightforwardly generalize to this case. Instead the analytic properties of the retarded Green’s function of conserved currents (or of the stress-energy tensor) will be used, and the theory will be assumed to become conformal in the UV. The method is general and applicable to both cosmology and condensed matter systems. As a concrete example we will consider the EFT of conformal superfluids, which describes the universal low-energy dynamics of CFTs at large chemical potential, and we will derive inequalities on the coefficients of the operators, in three spacetime dimensions, at NLO and NNLO.