Improved late-time fits with wavelet extensions of ΛCDM

We parametrize the Hubble function by adding Hermitian wavelets to the Hubble radius of $\Lambda$ cold dark matter ($\Lambda$CDM). This construction enables the Hubble function to oscillate around $\Lambda$CDM at late times while preserving the angular diameter distance to the last scattering. We perform parameter inference and model selection at the background level using a wide range of cosmological observations. We find that baryon acoustic oscillation (BAO) data play a central role in constraining the wavelet parameters. In particular, we focus on the differences between SDSS and DESI BAO data sets. Wavelet models consistently provide a better fit when either BAO data set is included. DESI-BAO prefers wavelets centred around $z \sim 0.7$, while SDSS-BAO prefers higher redshifts ($z > 1$), driven by discrepancies in their $D_H / r_{\rm d}$ measurements at $z = 0.51$ and $z \sim 2.3$. We also analyse the consequences for a dynamical dark energy component derived from the wavelet modifications. The dark energy density is found to oscillate by construction and can become negative at large redshifts ($z \gtrsim 2$) in response to the SDSS-BAO data. Notably, the early Universe constraints, including those on the matter density and Hubble constant, remain essentially unchanged. Our results indicate that wavelet-based deviations are favoured in the late Universe, with DESI-BAO leading to a significant improvement of more than $3\sigma$ in the fit. These findings suggest that localized oscillatory features in the expansion history may help reconcile tensions in low-redshift data without disrupting early-Universe consistency.