  Using the fact that the comoving angular diameter distance to the last
scattering surface is strictly constrained almost model independently, we show
that, for any model agreeing with the standard $\Lambda$CDM model on its
background dynamics at $z\sim0$ and size of the comoving sound horizon at last
scattering, the deviations of the Hubble radius from the one of the standard
$\Lambda$CDM model must be a member of the set of admissible wavelets. The
family of models characterized by this framework also offers nontrivial
oscillatory behaviours in various functions that define the kinematics of the
Universe, even when the wavelets themselves are very simple. We also discuss
the consequences of attributing these kinematics to, first, dark energy, and
second, varying gravitational coupling strength. Utilizing some simplest
wavelets, we demonstrate the competence of this framework in describing the
baryon acoustic oscillation (BAO) data without any modifications to the
agreement with cosmic microwave background measurements. This framework also
provides a natural explanation for the bumps found in nonparametric
observational reconstructions of the Hubble parameter and dark energy density
as compensations of the dips suggested by some BAO data, and questions the
physical reality of their existence. We note that utilizing this framework on
top of the models that agree with both the cosmic microwave background and
local $H_0$ measurements but are held back by BAO data, one may resurrect these
models through the wiggly nature of wavelets that can naturally accommodate the
BAO data. Finally, we also suggest narrowing the plausible set of admissible
wavelets to further improve our framework by imposing conditions from expected
kinematics of a viable cosmological model or first principle fundamental
physics such as energy conditions.
