Cosmic low temperature physics: Making molecules on stardust

The lightest, simplest and the most abundant molecule in the universe, molecular hydrogen, is one of the most important in the physical and chemical evolution of the Cosmos: it is an essential ingredient in star formation by facilitating the cooling of a gravitationally collapsing cloud; and it enters, either neutral or charged, in most reactions to produce other molecules in space. Through its transitions, we learn about the physical and chemical environments it finds itself in. Its formation requires the help of sub-micron size dust grains, particles in interstellar space that once originated in the ejecta of late type stars, or in novae and supernovae. Until a decade and a half ago, little was known how this molecule is formed in interstellar space. Here I review experimental and theoretical studies of the formation of astrophysically important molecules, and molecular hydrogen in particular, on analogs of interstellar dust grains at low temperature. I will show that these studies touch important and still little understood aspects of elementary processes of atoms and molecules on surfaces at low temperature.