Abstract
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.
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