  We study the impact of three-body physics in quenched unitary Bose gases,
focusing on the role of the Efimov effect. Using a local density model, we
solve the three-body problem and determine three-body decay rates at unitary,
finding density-dependent, log-periodic Efimov oscillations, violating the
expected continuous scale-invariance in the system. We find that the breakdown
of continuous scale-invariance, due to Efimov physics, manifests also in the
earliest stages of evolution after the interaction quench to unitarity, where
we find the growth of a substantial population of Efimov states for densities
in which the interparticle distance is comparable to the size of an Efimov
state. This agrees with the early-time dynamical growth of three-body
correlations at unitarity [Colussi {\em et al}., Phys. Rev. Lett. 120, 100401
(2018)]. By varying the sweep rate away from unitarity, we also find a
departure from the usual Landau-Zener analysis for state transfer when the
system is allowed to evolve at unitarity and develop correlations.
