  Lead halide perovskites possess high photoluminescence (PL) efficiency and
strong electron-phonon interactions, and therefore the optical cooling using
up-conversion PL has been expected. We investigate anti-Stokes PL from
green-luminescent Cs$_4$PbBr$_6$, whose origin is attributable to CsPbBr3
nanostructures embedded in a Cs$_4$PbBr$_6$ crystal. Because of the high
transparency, low refractive index, and high stability of Cs$_4$PbBr$_6$, the
green PL displays high external quantum efficiency without photo-degradation.
Time-resolved PL spectroscopy reveals the excitonic behaviors in recombination
process. The shape of the PL spectrum is almost independent of excitation
photon energy, which means that the spectral width is determined by homogeneous
broadening. We demonstrate that the phonon-assisted process dominates the
Urbach tail of optical absorption and anti-Stokes PL at room temperature.
Anti-Stokes PL is observed down to 70 K. We determine the temperature
dependence of the Urbach energy and estimate the strength of the
electron-phonon coupling. Our spectroscopic data show that CsPbBr3
nanostructures have potentially useful features for optical cooling.
