  The microscopic origin of slow carrier cooling in lead-halide perovskites
remains debated, and has direct implications for applications. Slow carrier
cooling has been attributed to either polaron formation or a hot-phonon
bottleneck effect at high excited carrier densities (> 10$^{18}$ cm$^{-3}$).
These effects cannot be unambiguously disentangled from optical experiments
alone. However, they can be distinguished by direct observations of ultrafast
lattice dynamics, as these effects are expected to create qualitatively
distinct fingerprints. To this end, we employ femtosecond electron diffraction
and directly measure the sub-picosecond lattice dynamics of weakly confined
CsPbBr$_3$ nanocrystals following above-gap photo-excitation. The data reveal a
light-induced structural distortion appearing on a time scale varying between
380 fs to 1200 fs depending on the excitation fluence. We attribute these
dynamics to the effect of exciton-polarons on the lattice, and the slower
dynamics at high fluences to slower hot carrier cooling, which slows down the
establishment of the exciton-polaron population. Further analysis and
simulations show that the distortion is consistent with motions of the
[PbBr$_3$]$^{-}$ octahedral ionic cage, and closest agreement with the data is
obtained for Pb-Br bond lengthening. Our work demonstrates how direct studies
of lattice dynamics on the sub-picosecond timescale can discriminate between
competing scenarios, thereby shedding light on the origin of slow carrier
cooling in lead-halide perovskites.
