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 $\mathrm{\Lambda }$CDM model on its background dynamics at $z\sim 0$ and size of the comoving sound horizon at last scattering, the deviations of the Hubble radius from the one of the standard $\mathrm{\Lambda }$CDM model must be a member of the set of admissible wavelets. The family of models characterized by this framework also offers nontrivial oscillatory behaviors 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.

• Received 4 August 2022
• Accepted 23 May 2023

DOI:https://doi.org/10.1103/PhysRevD.107.123526