Do we need wavelets in the late Universe?

TL;DR

This paper introduces wavelet-modified Hubble functions to explore late-time oscillations in the universe's expansion, finding that BAO data favor wavelets and improve fit quality, especially with DESI data.

Contribution

It proposes a novel wavelet-based parametrization of the Hubble function that captures late-time oscillations without affecting early universe constraints.

Findings

Wavelets improve fit to BAO data, especially with DESI.

Wavelet center prefers z~0.7 with DESI, higher z with SDSS.

Dark energy density oscillates and can be negative at high z.

Abstract

We parameterize the Hubble function by adding Hermitian wavelets to the Hubble radius of $\Lambda$CDM. This allows us to build Hubble functions that oscillate around $\Lambda$CDM at late times without modifying its angular diameter distance to last scattering. We perform parameter inference and model selection procedures on these new Hubble functions at the background level. In our analyses consisting of a wide variety of cosmological observations, we find that baryon acoustic oscillations (BAO) data play a crucial role in determining the constraints on the wavelet parameters. In particular, we focus on the differences between SDSS- and DESI-BAO datasets and find that wavelets provide a better fit to the data when either of the BAO datasets is present. However, DESI-BAO has a preference for the center of the wavelets to be around $z \sim 0.7$, while SDSS-BAO prefers higher redshifts of $z > 1$. This difference appears to be driven by the discrepancies between these two datasets in their $D_H / r_{\rm d}$ measurements at $z = 0.51$ and $z \sim 2.3$. Finally, we also derive the consequences of the wavelets on a dark energy component. We find that the dark energy density oscillates by construction and also attains negative values at large redshifts ($z\gtrsim2$) as a consequence of the SDSS-BAO data. We conclude that while the early universe and the constraints on the matter density and the Hubble constant remain unchanged, wavelets are favored in the late universe by the BAO data. Specifically, there is a significant improvement at more than $3\sigma$ in the fit when new DESI-BAO data are included in the analysis.