Andrey V. Kravtsov
Ph.D., Astronomy/Computer Science, New Mexico State University, 1999
Study of structure formation in the Universe is an area of forefront research in astrophysics. The early evolution, when the seed fluctuations are small, can be calculated analitycally on a piece of paper without the help of large supercomputers. As the fluctuations grow in their amplitude, the evolution becomes too complex and theorists have to use computers to follow the subsequent evolution.
A typical simulation follows evolution of matter in a large box which expands at the same rate as the Universe itself. The box thus always encompasses the same mass. Over the period of time evolved in simulations the Universe expands by a factor of more than 50 and so does the simulation box (you can find a nice illustration of this here). In order to make it simpler to visualize the formation of structures, the expansion can be taken out so that the simulation box appears static. In professional lingo, the system of coordinates that expands (or co-moves) with the Universe is called the comoving coordinate system.
As the Universe expands, galaxies become more and more distant from each other. For an observer, such as ourselves, it appears that all other galaxies fly away from us. The further the galaxy, the faster it appears to recede. This recession affects the light emitted by the distant galaxies, stretching the wavelengths of emitted photons due to the Doppler redshift effect. The distance between galaxies is proportionalto the measure of this effect 1+z, where z is what astronomers call redshift. The redshift can be measured for each object if its spectrum is measured.
In addition, it takes a very long time (up to several billion years) for the light from the most distant galaxies and quasars to reach us. Not only the light we receive from these objects is redshifted, but we also see these objects as they were during the early stages in the evolution of the Universe. In this sense, the redshift z provides a universal clock and can be used as a measure of time. Observations of distant galaxies is much like a time travel into the past.
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