The Evolution of the Intergalactic Medium

The bulk of cosmic matter resides in a dilute reservoir that fills the space between galaxies, the intergalactic medium (IGM). The history of this reservoir is intimately tied to the cosmic histories of structure formation, star formation, and supermassive black hole accretion. Our models for the IGM at intermediate redshifts (2<z<5) are a tremendous success, quantitatively explaining the statistics of Lyman-alpha absorption of intergalactic hydrogen. However, at both lower and higher redshifts (and around galaxies) much is still unknown about the IGM. We review the theoretical models and measurements that form the basis for the modern understanding of the IGM, and we discuss unsolved puzzles (ranging from the largely unconstrained process of reionization at high-z to the missing baryon problem at low-z), highlighting the efforts that have the potential to solve them.