Overview

• The very early universe In this stage, some mechanism, such as cosmic inflation is responsible for establishing the initial conditions of the universe: homogeneity, isotropy and flatness.
• The primordial plasma The universe is dominated by radiation for most of this stage, and due to free-streaming structures can't be amplified gravitationally. Nonetheless, important evolution takes place, such as big bang nucleosynthesis creates the primordial elements and the cosmic microwave background is emitted. The detailed anisotropy structure of the cosmic microwave background is also created in this epoch.
• Non-linear growth of structure As the dense regions become denser, the linear approximation describing density inhomogeneities begins to break down – adjacent particles may even begin to cross in caustics – and a more detailed treatment, using the full Newtonian theory of gravity, becomes necessary. (Aside from the background expansion of the universe, which is due to general relativity, evolution on these comparatively small scales is usually well approximated by the Newtonian theory.) This is where structures, such as galaxy clusters and galaxy haloes begin to form. Still, in this regime only gravitational forces are significant because dark matter, which is thought to have very weak interactions, is the dominant player.
• "Gastrophysical" evolution The final step of the evolution is when electromagnetic forces become important in the evolution of structure, where baryonic matter clusters densely, as in galaxies and stars. In some cases, such as active galactic nuclei and quasars, Newtonian theory works poorly and general relativity becomes significant. It is called "gastrophysical" because of its complexity: many different, complicated effects, including gravity, magnetohydrodynamics and nuclear reactions must be taken into account.

  Linear structure

  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 mysterious form of matter known as dark matter. Dark matter interacts through the force of gravity, but it isn't composed of baryons and it's known with very high accuracy that it doesn't emit or absorb radiation. It may be composed of particles that interact through the weak interaction, such as neutrinos, but it can't be composed entirely of the three known kinds of neutrinos (although some have suggested it's a sterile neutrino). Recent evidence suggests that there's about five times as much dark matter as baryonic matter, and thus the dynamics of the universe in this epoch are dominated by dark matter.
     Dark matter plays a key role in structure formation because it feels only the force of gravity: the gravitational Jeans instability which allows compact structures to form isn't opposed by any force, such as radiation pressure. 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 physics of structure formation in this epoch is particularly simple, as dark matter perturbations with different wavelengths evolve independently. As the Hubble radius grows in the expanding universe, it encompasses larger and larger perturbations. During matter domination, all causal dark matter perturbations grow through gravitational clustering. However, the shorter-wavelength perturbations that are encompassed during radiation domination have their growth retarded until matter domination. At this stage, luminous, baryonic matter is expected to simply mirror the evolution of the dark matter, and their distributions should closely trace one another.
     It is a simple matter to calculate this "linear power spectrum" and, as a tool for cosmology, it's of comparable importance to the cosmic microwave background. The power spectrum has been measured by galaxy surveys, such as the Sloan Digital Sky Survey, and by surveys of the Lyman-α forest. Since these surveys observe radiation emitted from galaxies and quasars, they don't directly measure the dark matter, but the large scale distribution of galaxies (and of absorption lines in the Lyman-α forest) is expected to closely mirror the distribution of dark matter. This depends on the fact that galaxies will be larger and more numerous in denser parts of the universe, whereas that'll be comparatively scarce in rarefied regions.

  Non-linear structure

  When the perturbations have grown sufficiently, a small region might become substantially more dense than the mean density of the universe. At this point, the physics involved becomes substantially more complicated. When the deviations from homogeneity are small, the dark matter may be treated as a pressureless fluid and evolves by very simple equations. In regions which are significantly more dense than the background, the full Newtonian theory of gravity must be included. (The Newtonian theory is appropriate because the masses involved are much less than those required to form a black hole, and the speed of gravity may be ignored as the light-crossing time for the structure is still smaller than the characteristic dynamical time.) One sign that the linear and fluid approximations become invalid are that dark matter starts to form caustics in which the trajectories of adjacent particles cross, or particles start to form orbits. These dynamics are generally best understood using N-body simulations (although a variety of semi-analytic schemes, such as the Press-Schechter formalism, can be used in some case). While in principle these simulations are quite simple, in practice they're very difficult to implement, as they require simulating millions or even billions of particles. Moreover, despite the large number of particles, each particle typically weighs 10⁹ solar masses and discretization effects may become significant. The largest such simulation is the recent Millennium simulation.
     The result of N-body simulations suggest that the universe is composed largely of voids, whose densities might be as low as one tenth the cosmological mean. The matter condenses in large filaments and haloes which have an intricate web-like structure. These form galaxy groups, clusters and superclusters. While the simulations appear to agree broadly with observations, their interpretation is complicated by the understanding of how dense accumulations of dark matter spur galaxy formation. In particular, many more small haloes form than we see in astronomical observations as dwarf galaxies and globular clusters. This is known as the galaxy bias problem, and a variety of explanations have been proposed. Most account for it as an effect in the complicated physics of galaxy formation, but some have suggested that it's a problem with our model of dark matter and that some effect, such as warm dark matter, prevents the formation of the smallest haloes.

  Gastrophysical evolution

  The final stage in evolution comes when baryons condense in the centers of galaxy haloes to form galaxies, stars and quasars. A paradoxical aspect of structure formation is that while dark matter greatly accelerates the formation of dense haloes, because dark matter doesn't have radiation pressure, the formation of smaller structures from dark matter is impossible because dark matter can't dissipate angular momentum, whereas ordinary baryonic matter can collapse to form dense objects by dissipating angular momentum through radiative cooling. Understanding these processes is an enormously difficult computational problem, because they can involve the physics of gravity, magnetohydrodynamics, atomic physics, nuclear reactions, turbulence and even general relativity. In most cases, it isn't yet possible to perform simulations that can be compared quantitatively with observations, and the best that can be achieved are approximate simulations that illustrate the main qualitative features of a process such as star formation.
  

  Modelling structure formation

  Cosmological perturbations

  Much of the difficulty, and many of the disputes, in understanding the large-scale structure of the universe can be resolved by understanding the choice of gauge in general relativity better. By the scalar-vector-tensor decomposition, the metric includes four scalar perturbations, two vector perturbations, and one tensor perturbation. Only the scalar perturbations are significant: the vectors are exponentially suppressed in the early universe, and the tensor mode makes only a small (but important) contribution in the form of primordial gravitational radiation and the B-modes of the cosmic microwave background polarization. Two of the four scalar modes may be removed by a physically meaningless coordinate transformation. Which modes are eliminated determine the infinite number of possible gauge fixings. The most popular gauge is Newtonian gauge (and the closely related conformal Newtonian gauge), in which the retained scalars are the Newtonian potentials Φ and Ψ, which correspond exactly to the Newtonian potential energy from Newtonian gravity. Many other gauges are used, including synchronous gauge, which can be an efficient gauge for numerical computation (it is used by CMBFAST). Each gauge still includes some unphysical degrees of freedom. There is a so-called gauge-invariant formalism, in which only gauge invariant combinations of variables are considered.

  Inflation and 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 $ho(mathbf)$,
  
  where $n\_s-1$ 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.
  

  Further Information

  Get more info on 'Structure Formation'.

  
  

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