The size of the primordial density fluctuations is known by a combination of theory (i.e., inflation) and observation (i.e., the cosmic microwave background (CMB, T = 2.72548(57) K (Fixsen 2009))) (see Wikipedia: Structure formation: Before the first structures).????
It is a case of the rich getting richer and the poor getting poorer.
The higher density primordial density fluctuations collapse under their self-gravity to became gravitationally bound systems.
The lower density primordial density fluctuations to became sitll lower in relative density and the lowest ones evolved to becoming cosmic voids: regions of relative low density.
Note, the density between gravitationally bound systems was declining in general because of the overall expansion of the universe. The universal expansion is a major background effect opposing the clumping of the matter. It must be considered a given in all our discussions as it is in all calculations of the large-scale structure.
Note, we do NOT see dark matter (so far), except through its gravitational effect on baryonic matter which we do see in emitted electromagnetic radiation (EMR).
Recall, baryonic matter is ordinary ordinary matter made of protons, neutrons, and electrons.
Note, the initial baryonic matter was created by Big Bang nucleosynthesis (cosmic time ∼ 10--1200 s ≅ 0.17--20 m) and had the primordial cosmic composition (which is also almost cosmic present intergalactic medium composition: fiducial values by mass fraction: 0.75 H, 0.25 He-4, 0.001 D, 0.0001 He-3, 10**(-9) Li-7).
Since then interstellar medium (ISM) of has been enriched in metallicity (Z). In the modern/local observable universe is cosmic composition (meaning inside modern galaxies: fiducial values by mass fraction: 0.73 H, 0.25 He-4, ∼ 0.02 metals). The evolution of metallicity (Z) is discussed in Cosmology file: metallicity_evolution.html.
Such N-body simulations in the context of the Λ-CDM model (the current standard cosmological model (c.1995--): Scott 2018) have always done a good 1st order job in reproducing the statistical properties of the observed large-scale structure. Note, the Λ-CDM model fits the observable universe so well overall, that any replacement cosmological model will have to have similar properties to the Λ-CDM model for the calculation of the large-scale structure.
See N-body simulation videos below (local link / general link: n_body_videos.html).
For formation of the first stars and galaxies is called cosmic dawn (AKA reionization era, z∼6--20, cosmic time ∼ 150 Myr--1 Gyr in the Λ-CDM model).
The period between recombination era t = 377,770(3200) Jyr = 1.192*10**13 s (z = 1089.80(21)) (where the cosmic microwave background (CMB, T = 2.72548(57) K (Fixsen 2009)) formed an cosmic dawn is called the cosmic dark age (∼ 377 kyr (z ≅ 1100) -- ∼< 200 Myr (z ≅ 20)).
So N-body simulations though extremely useful in understanding much structure formation are NOT adequate to to give us the actual existing large-scale structure of the observable universe which is now often called the cosmic web.
The pressure forces include ideal gas law pressure, radiation pressure, and magnetic pressure (which if nothing else helps to launch relativistic bipolar jets from central supermassive black hole, and thus provides AGN feedback to structure formation).
The galaxies themselves became organized in the larger large-scale structure: i.e., the cosmic web consisting of galaxy groups (⪅ 50 large galaxies), galaxy clusters (⪆ 50 large galaxies , galaxy superclusters, galaxy filaments, galaxy walls, and cosmic voids.
For an example galaxy cluster, see the figure below (local link / general link: galaxy_cluster_RXC_J0142.9+4438.html).
Galaxies NOT in galaxy groups and galaxy clusters are called field galaxies.
Note, galaxies, galaxy groups, and galaxy clusters are usually gravitationally bound systems. The other structures listed above are usually NOT gravitationally bound systems.
The statistics for dwarf galaxies are much less certain and will probably be continually revised for a long time to come.
Note, the initial baryonic matter was created by Big Bang nucleosynthesis (cosmic time ∼ 10--1200 s ≅ 0.17--20 m) and had the primordial cosmic composition (which is also almost cosmic present intergalactic medium composition: fiducial values by mass fraction: 0.75 H, 0.25 He-4, 0.001 D, 0.0001 He-3, 10**(-9) Li-7).
The most basic morphological classification for large galaxies is the Hubble sequence (see Galaxies file: galaxy_hubble_sequence.html). A extension of the Hubble sequence is the de Vaucouleurs system (see Galaxies file: galaxy_vaucouleurs.html).
Reproducing all the observed galaxy types with the correct statistical distribution is one of the ultimate goals of structure formation computer simulations. Great progress has been made toward this ultimate goal.
"Cold" in this context means moving slow relative to the vacuum light speed c = 2.99792458*10**5 km/s ≅ 3*10**5 km/s: i.e., at nonrelativistic velocities relative to the local comoving frames (see frame_hierarchy_astro.html: Comoving Frames).
Cold dark matter is needed to get the clumping properties needed for the observed large-scale structure.
Without cold dark matter, the baryonic matter would probably still clump to form stars as we know them, but galaxies and the rest of large-scale structure would look very different from what we see.
Note, there MAY be exotic hot dark matter (dark matter moving at relativistic velocities) and warm dark matter (at intermediate velocities), but these dark matter forms can only be of secondary importance in structure formation.
Actually, neutrinos forming the cosmic neutrino background (a relic of the Big Bang from before Big Bang nucleosynthesis (BBN)) were originally a form of hot dark matter, but they lost kinetic energy in a manner similar to that of cosmologically redshifting photons and became a minor contribution to cold dark matter.
We are trying to calculate simulated large-scale structure that has the SAME statistical properties as that of the large-scale structure: e.g., same average number of galaxies of each type per unit volume, same average number of galaxy clusters per unit volume, etc.
Why CAN'T we calculate our observable universe?
The exact primordial density fluctuations from Big Bang era in the observable universe CANNOT be completely known. The cosmic microwave background (CMB) T = 2.7260(13) K gives information on the surface of last scattering: i.e., the sphere surrounding us from which the CMB photons that actually reach us last scattered on their radial paths to us.
For the rest of the locations in the observable universe, we have to assume a distribution of primordial density fluctuations inferred from what the CMB and inflation.
Of course, a computer simulation of structure formation starts from a particular set of simulated primordial density fluctuations, that set is just drawn randomly from the assumed istribution of primordial density fluctuations.
Circa 2025, trhere is NO reason to believe that we will NOT eventually match the statistical properties of the observable universe to high accuracy provided we can the right overall cosmological model.
Do we have it now. Probably NOT, at least NOT exactly. See the next item.
There are some tensions betwen structure formation computer simulations and observations, but NO falsifications currently.
Digression on jargon: A falsification is a discrepancy between theory and observation sufficiently large that one judges the theory to be wrong.
A tension is a discrepancy that does NOT cause one to judge the theory as wrong. The discrepancy may be due uncertainties in the observations or in the application of the theory.
Tensions suggest there might be a problem with a theory, but more work is needed to show if that is true. More work hopefully will cause the tensions to go away OR turn them into falsifications. Either way, progress.
