  We investigate a modified cosmological model aimed at addressing the Hubble
tension, considering revised dynamics in the late Universe. The model
introduces a parameter $c$ affecting the evolution equations, motivated by a
modified Poisson algebra inspired by effective Loop Quantum Cosmology. Our
analysis includes diverse background datasets such as Cosmic Chronometers,
Pantheon+ Type Ia Supernovae (with and without the SH0ES calibration), SDSS,
DESY6 and DESI Baryon Acoustic Oscillations, and background information of the
Cosmic Microwave Background. We find that the model alleviates the Hubble
tension in most of the dataset combinations, with cases reducing discrepancies
to below $1\sigma$ when including SH0ES. However, the model exhibits minimal
improvement in the overall fit when compared to $\Lambda$CDM, and Bayesian
evidence generally favors the standard model. Theoretical foundations support
this approach as a subtle adjustment to low-redshift dynamics, suggesting
potential for further exploration into extensions of $\Lambda$CDM. Despite
challenges in data fitting, our findings underscore the promise of small-scale
modifications in reconciling cosmological tensions.
