  The structure of dielectric perovskite BaZrO$_3$, long known to be cubic at
room temperature without any structural phase transition with variation of
temperature, has been recently disputed to have different ground state
structures with lower symmetries involving octahedra rotation. The
pressure-dependent Raman scattering measurements can identify the hierarchy of
energetically-adjacent polymorphs, helping in turn understand its ground state
structure at atmospheric pressure. Here, Raman scattering spectra of
high-quality BaZrO$_3$ single crystals grown by the optical floating zone
method are investigated in a pressure range from 1 atm to 42 GPa. First, based
on the analyses of the infrared and Raman spectra measured at the atmosphere,
it is found that all observed vibrational modes can be assigned according to
the cubic $Pm\bar{3}m$ structure. In addition, by applying pressure, two
structural phase transitions are found at 8.4 and 19.2 GPa, one from the cubic
to the rhombohedral $R\bar{3}c$ phase and the other from the rhombohedral to
the tetragonal $I4/mcm$ phase. Based on the two pressure-induced structural
phase transitions, the true ground state structure of BaZrO$_3$ at room
temperature and ambient pressure is corroborated to be cubic while the
rhombohedral phase is the closest second.
