The Sound Speed of the Effective Spin Fluid: Where the Squared Sound Speed Changes Sign and What It Costs Perturbations

For a radiation-like component the numerator of the squared sound speed vanishes at r = 0.100, and the quantity is negative over a fraction 0.400 of the density range up to the bounce. For stiff matter the zero sits at r = 0.167. For dust the squared sound speed is negative over a fraction 0.500 of the range, essentially the entire sub-maximal-density interval, because a pressureless component acquires its effective pressure entirely from the correction term. The pole at r = 1/2, where the effective density is stationary, makes the effective sound speed diverge there in all cases: a definite sign that the effective-fluid language, not necessarily the physics, is failing at that surface. The study is a computation from stated assumptions, performed by the accompanying script; it is simulated, not measured.