Cold molecular hydrogen

Due to its simplicity, H₂ constitutes a perfect tool for testing fundamental physics: testing quantum electrodynamics, determining fundamental constants, or searching for new physics beyond the Standard Model. H₂ has a huge advantage over the other simple calculable systems of having a set of a few hundred ultralong living rovibrational states, which implies the ultimate limit for testing fundamental physics with H₂ at a relative accuracy level of 10^-24. The present experiments are far from this limit. I will present our results and ongoing projects aimed at exploring this huge potential with cold H₂. I will present our recent H₂ spectra collected with a high-finesse optical cavity cooled down to a deep cryogenic temperature (T = 5 K). I will present our new ongoing project aiming at trapping cold H₂.