The basic picture is hierarchical structure formation. In this bottom-up picture, galaxies (starting from initial small galaxies) underwent continuing galaxy mergers resulting in the large range of galaxies of the modern observable universe. The galaxy merger process continues.
The galaxies themselves became organized in the large-scale structure: i.e., the cosmic web consisting of galaxy walls, galaxy filaments, galaxy clusters, galaxy groups, and voids.
For an example galaxy cluster, see the figure below (local link / general link: galaxy_cluster_RXC_J0142.9+4438.html).
How did proto-galaxies form?
The rich got richer and the poor got poorer.
In the more-dense initial density fluctuations, there were gravitational runaways of matter (∼ 85 % of it being dark matter) to form clumps (dense regions) called dark matter halos where the proto galaxies formed.
In the less-dense initial density fluctuations, the dark matter did NOT clump and large voids formed.
Note, 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.
Now to 1st order, dark matter and its gravity determine everything since the dark matter is ∼ 85 % of the matter in the observable universe and it interacts with itself and baryonic matter only very weakly if at all, EXCEPT through gravity.
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).
The baryonic matter to 1st order just follows the dark matter pulled along by the dark matter's gravity.
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).
A key point about the dark matter: it was cold dark matter (CDM).
"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.
Because of the dominance of dark matter over baryonic matter, large-scale structure to 1st order can be understood with just dark matter and gravity using N-body simulations which include particles interacting through gravity alone.
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).
To fully understand large-scale structure, we must understand how the baryonic matter clumps into observable galaxies, etc. This is much more complicated than just studying dark matter since baryonic matter interacts through pressure forces as well as gravity.
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).
Note, you can only model the statistical properties of large-scale structure since initial conditions of the matter distribution (the aforesaid fluctuations) are only known statistically and, in fact, only known from theory and the aforementioned inflation being the adequate theory currently. Inflation is shown to be adequate since its predicted fluctuations do allow the observed statistical properties to be reproduced to within uncertainty so far.
Note, in calculations of large-scale structure we are NEVER trying to calculate our observable universe exactly as we see it.
We are trying to calculate simulated large-scale structure that as 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 initial density fluctuations left from the Big Bang era CANNOT be known. We can only theorize their statistical properties, and so only calculate the statistical properties of the observable universe that evolves from them.
But we have a good theory of those fluctuations since we do calculate the statistical properties of the observable universe pretty well.
There is NO reason at present 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.
Since circa 1998, the Λ-CDM model of cosmology has been the main context for structure formation.
There are some tensions for structure formation, 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.
Actually, the Λ-CDM model is suffering a severe tension in regard to the Hubble constant. It seems likely that the Λ-CDM model will have to be revised and the revision may or may NOT have the same name. We take up this story in IAL 30: Cosmology. See also big_bang_cosmology_limitations.html.
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Cosmology file

large_scale_structure_formation_outline.html

An Outline of the Story of Large-Scale Structure Formation