Astrochemistry of the molecular gas in Dusty Star-Forming Galaxies at the Cosmic Noon

FIR and submm observations have established the fundamental role of dust-obscured star formation in the assembly of stellar mass over the past 12 billion years. At z between 2 and 4, the bulk of star formation is enshrouded in dust, and dusty star forming galaxies (DSFGs) contain about half of the total stellar mass density. Star formation develops in dense molecular clouds, and is regulated by a complex interplay between all the ISM components that contribute to the energy budget of a galaxy: gas, dust, cosmic rays, interstellar electromagnetic fields, gravitational field, dark matter. Molecular gas is the actual link between star forming gas and its complex environment, providing by far the richest amount of information about the star formation process. However, molecular lines interpretation requires complex modeling of astrochemical networks, which regulate the molecular formation and establishes molecular abundances in a cloud, and a modeling of the physical conditions of the gas in which molecular energy levels become populated. This paper critically reviews the main astrochemical parameters needed to get predictions about molecular signals in DSFGs. We review the current knowledge and the open questions about the interstellar medium of DSFGs, outlying the key role of molecular gas as a tracer and shaper of the star formation process.