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STRUCTURE FORMATION

It has been suggested that this article or section be merged into Large-scale structure of the cosmos. (Discuss)

Structure formation refers to a fundamental problem in physical cosmology. The universe, as is now known from observations of the cosmic microwave background radiation, began in a hot, dense, nearly uniform state approximately 11 billion years ago. However, looking in the sky today, we see structures on all scales, from stars and planets to galaxies and, on much larger scales still, galaxy clusters, and enormous voids between galaxies. How did all of this come about from the nearly uniform early universe?

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Cosmological Fluctuations

Structure formation includes two key ingredients. The first is the realization that while observations indicate that the cosmic microwave background radiation is nearly uniform, there are very small temperature fluctuations at one part in 100,000. To put this in perspective, the same level of fluctuations on a topographic map of the United States would show no feature higher than a few meters high. However, these fluctuations are critical, because they provide the seeds from which the largest structures within the universe can grow and eventually collapse to form galaxies and stars. COBE(Cosmic Background Explorer) provided the first detection of the intrinsic fluctuations in the cosmic microwave background radiation in the 1990s, and confirmed that these fluctuations were consistent with the predictions of the inflationary model of the universe.

Dark Matter

The second key ingredient is dark matter. One of the key realizations made by cosmologists in the 1970s and 1980s was that the majority of the matter content of the universe was composed not of atoms, but rather a strange mysterious form of matter known as dark matter. Dark matter interacts through the force of gravity, but does not emit or absorb radiation, and hence interacts only very feebly via the weak interaction (at best) with itself or with ordinary matter.

Dark matter turns out to play a key role in accelerating the process of structure formation precisely because it feels only the force of gravity. As a result, dark matter begins to collapse into a complex network of dark matter halos well before ordinary matter, which is impeded by pressure forces. Without dark matter, the epoch of galaxy formation would occur substantially later in the universe than is observed.

The Millennium Simulation

The famous millennium simulation [1] does to some extent explain how large scale structure can be formed from initial fluctuation.

Initial Conditions

The initial conditions for the universe are thought to arise from the scale invariant quantum mechanical fluctuations of cosmic inflation. The perturbation of the background energy density at a given point \rho(\mathbf{x},t) in space is then given by an isotropic, homogeneous Gaussian random field of mean zero. This means that the spatial Fourier transform of ρ – \hat{\rho}(\mathbf{k},t) has the following correlation functions

\langle\hat{\rho}(\mathbf{k},t)\hat{\rho}(\mathbf{k}',t)\rangle=f(k)\delta^{(3)}(\mathbf{k}-\mathbf{k'}),

where δ(3) is the three dimensional Dirac delta function and k=|\mathbf{k}| is the length of \mathbf{k}. Moreover, the spectrum predicted by inflation is nearly scale invariant, which means

\langle\hat{\rho}(\mathbf{k},t)\hat{\rho}(\mathbf{k}',t)\rangle=k^{n_s-1}\delta^{(3)}(\mathbf{k}-\mathbf{k'}),

where ns − 1 is a small number. Finally, the initial conditions are adiabatic or isentropic, which means that the fractional perturbation in the entropy of each species of particle is equal.