  For the spatially inhomogeneous, non-cutoff Boltzmann equation posed in the
whole space $\mathbb R^3_x$, we establish pointwise lower bounds that appear
instantaneously even if the initial data contains vacuum regions. Our lower
bounds depend only on the initial data and upper bounds for the mass and energy
densities of the solution. As an application, we improve the weakest known
continuation criterion for large-data solutions, by removing the assumptions of
mass bounded below and entropy bounded above.
