  Hydrogen oscillation into a dark-sector state $H'$ has recently been proposed
as a novel mechanism through which hydrogen can be cooled during the dark ages
-- without direct couplings between the Standard Model and dark matter. In this
work we demonstrate that the requisite mixing can appear naturally from a
microphysical theory, and argue that the startling deviations from standard
cosmology are nonetheless consistent with observations. A symmetric mirror
model enforces the necessary degeneracy between $H$ and $H'$, and an additional
twisted $B+L'$ symmetry dictates that $H$-$H'$ mixing is the leading connection
between the sectors. We write down a UV completion where $\sim$ TeV-scale
leptoquarks generate the partonic dimension-12 mixing operator, thus linking to
the energy frontier. With half of all $H$ atoms oscillating into $H'$, the
composition of the universe is scandalously different during part of its
history. We qualitatively discuss structure formation: both the modifications
to it in the Standard Model sector and the possibility of it in the mirror
sector, which has recently been proposed as a resolution to the puzzle of early
supermassive black holes. While the egregious loss of SM baryons mostly
self-erases during reionization, to our knowledge this is the first model that
suggests there should be missing baryons in the late universe, and highly
motivates a continued, robust observational program of high-precision searches
for cosmic baryons.
