Parametrizing the Hubble function instead of dark energy: Many possibilities

In the present article, we propose a very simple parametrization of the Hubble function without parametrizing the dark components of the Universe. One of the novelties of the parametrization is that it may include a wide variety of the cosmological models, such as dark energy (both noninteracting and interacting fluids), modified gravity, cosmological matter creation, and other known scenarios. The model is constrained with the latest astronomical probes from Hubble parameter measurements, three distinct versions of type Ia Supernovae ($\mathrm{Pantheon}+$, DESY5, Union3) and baryon acoustic oscillations from Sloan Digital Sky Survey and Dark Energy Spectroscopic Instrument data releases 1 and 2. Our results suggest a mild deviation from the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmological model for most of the combined datasets. We also find that our model is thermodynamically consistent and performs well in the model comparison tests.