Cosmology SimulationsThe cosmological scales are the largest and require boundary conditions. Furthermore, if we wish to model our observable universe, consideration must be made for the expansion. At these scales we investigate the large scale structure of the universe, which not only provide information regarding the density of the components within the universe, but also can provide a wealth of information on the early universe and the Big Bang.
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The expansion of the universe
Most cosmological simulations that accurately model our universe will require expansion effects. An exaggerated example of this expansion can be seen below. Note that the distance between neighbouring objects grow unless the particles are initially close together such that gravitational forces can overcome the expansion.
Formation of large scale structure & The correlation function
Below is an example of a basic cosmological simulation where expansion effects have been used. A dynamic correlation function is also shown underneath the simulation. But first, what is a correlation function? We cannot simulate our universe exactly, so to extract useful information from our cosmological simulations, we wish to generate cosmological mass distributions that have the same statistical properties as our own universe! Therefore, we need tools that enable us to describe the density distributions of our universe, and our simulations. The correlation function allows us to do just this. Simply put, given a random galaxy, in a random location, the correlation function describes the probability that another galaxy will be found within a given distance [Peebles, 1980].
How can we interpret the correlation function?
Our simulation starts off with a random distribution of particles. As a result, when the simulation begins the correlation function is quite flat. However, after some time has elapsed, we see that the correlation function grows for small separations. This is a result of our particles constantly getting closer to each other and clumping. Furthermore, as the particles begin to collapse there are less particles at separations greater than 200 Mpc. This is represented by the decrease in the correlation function at large separations. Surveys of our own sky also find that galaxies are not randomly distributed in space but in fact gather in groups, clusters, or even large scale structures. More importantly baryon acoustic oscillations (BAO's; density fluctuations in the early universe) were expected to be observable in the matter distribution today. These BAO's have been successfully observed in the correlation function as 'wiggles.'