The Millennium Run, or Millennium Simulation (referring to its size) is a computer N-body simulation used to investigate how the distribution of matter in the Universe has evolved over time, in particular, how the observed population of galaxies was formed. It is used by scientists working in physical cosmology to compare observations with theoretical predictions. A basic scientific method for testing theories in cosmology is to evaluate their consequences for the observable parts of the universe. One piece of observational evidence is the distribution of matter, including galaxies and intergalactic gas, which are observed today. Light emitted from more distant matter must travel longer in order to reach Earth, meaning looking at distant objects is like looking further back in time. This means the evolution in time of the matter distribution in the universe can also be observed directly. The Millennium Simulation was run in 2005 by the Virgo Consortium, an international group of astrophysicists from Germany, the United Kingdom, Canada, Japan and the United States. It starts at the epoch when the cosmic background radiation was emitted, about 379,000 years after the universe began. The cosmic background radiation has been studied by satellite experiments, and the observed inhomogeneities in the cosmic background serve as the starting point for following the evolution of the corresponding matter distribution. Using the physical laws expected to hold in the currently known cosmologies and simplified representations of the astrophysical processes observed to affect real galaxies, the initial distribution of matter is allowed to evolve, and the simulation's predictions for formation of galaxies and black holes are recorded. Since the completion of the Millennium Run simulation in 2005, a series of ever more sophisticated and higher fidelity simulations of the formation of the galaxy population have been built within its stored output and have been made publicly available over the internet.

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