Type Ia Supernovae are standard candles of the Universe that enable us to probe the recent (z<1) expansion rate of the Universe. When their absolute magnitude is calibrated using, for instance Cepheids, SNeIa provide a direct measurement of the current expansion rate, also know as the Hubble-Lemaitre parameter H0. H0 can also be derived from high-redshift (early Universe) probes assuming a cosmological model. This way, Planck, in the context of LambdaCDM predicts a H0 value that is ~5sigma lower than the direct measurements from Cepheids and SNe. This could be a strong sign of new fundamental physics or the effect of a (potentially unknown) bias. We will investigate this so called H0-tension in this presentation in the context of potential systematic errors affecting, notably, the SNeIa distances. I will present recent and ongoing work relevant for that issue and show the prospect of using the Zwicky Transient Facility survey to provide new insights to solve this highly debated Cosmological result.
