  We investigate universal thermodynamics and quantum criticality of spin-1
bosons with strongly repulsive density-density and antiferromagnetic
spin-exchange interactions in a one-dimensional harmonic trap. From the
equation of state, we find that a partially-polarized core is surrounded by two
wings composed of either spin-singlet pairs or a fully spin-aligned
Tonks-Girardeau gas depending on the polarization. We describe how the scaling
behaviour of density profiles can reveal the universal nature of quantum
criticality and map out the quantum phase diagram. We further show that at
quantum criticality the dynamical critical exponent $z = 2$ and correlation
length exponent $\nu=1/2$. This reveals a subtle resemblance to the physics of
the spin-1/2 attractive Fermi gas.
