  BaZrO3 is a perovskite that remains in the simple cubic phase at all
temperatures, hence with no first-order Raman-active phonon mode allowed by
symmetry. Yet, it exhibits an intense Raman spectrum with sharp and
well-defined features. Here, we report the evolution of the Raman spectrum of
BaZrO3 single crystals in a broad temperature range (4--1200~K) and discuss its
origin with the support of detailed first-principle calculations of the lattice
dynamics. Phonon calculations are performed not only for the cubic phase of
BaZrO3, but also for the low-symmetry phases with octahedra tilts that have
been suspected to exist at the nanoscale. We show that the Raman spectrum shows
no direct evidence for these nanodomains, but can instead be explained by
classical second-order Raman scattering. We provide an assignment of the
dominant features to phonon modes combinations. In particular, we show that the
high frequency range of the spectrum is dominated by overtones and shows an
image of the phonon density of states corresponding to the stretching modes of
the oxygen octahedra.
