Cosmos 9: The Density of the Universe and Dark Matter

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The mass-energy density of the observable universe:
1. density parameter = Ω = rho/rho_crit.
2. For the Λ-CDM model, which is has Euclidean geometry (AKA flat geometry) the mean density is equal to the critical density = 3H_{0}**2/(8πG) = (9.20387*10**(-27))*h_70**2 km/m**3 = (1.35989*10**11)*h_70**2 M_☉/Mpc**3 .
3. The Planck-2018 values are rho_crit_p = 8.5227301511E-27 kg/m**3 = 1.2592481758E+11 M_☉/Mpc**3.
4. 10**11 M_☉ is about the mass of a largish galaxy including its dark matter. A very large galaxy has mass > ∼ golden mass = 10**12 M_☉ above which galaxies are usually quenched galaxies. The golden mass is NOT a law of nature, but just what the evolution of observable universe seems to have arrived at from a coincidence of many effects.
5. 1 Mpc is of order nearest neighbor galaxies, and so 10**11 M_☉/Mpc**3 is the natural unit cosmic density.
6. Due to large-scale structure or cosmic web (galaxies, galaxy clusters, galaxy superclusters, galaxy filaments galaxy walls and voids) the observed density only approaches the mean density on size scales of order usually 400 Mpc (see Wikipedia: Cosmological principle: Observations). But some structures are bigger. The current record is Hercules-Corona Borealis Great Wall with 3 Gpc which is a significant fraction of the comoving radius of the observable universe = 14.25 Gpc = 46.48 Gly (current value). This structure does NOT violate the cosmological principle it is thought. It is just a fluctuation in the part of the Big Bang universe we live in: i.e., the observable universe.
Wikipedia: Dark matter: Images: dark matter.
Astro: Lord Kelvin (1824--1907). See also Lord Kelvin (1824--1907)
English and Spanish Translation of Zwicky's (1933) The Redshift of Extragalactic Nebulae ((Die Rotverschiebung von extragalaktischen Nebeln): Heinz Andernach (translator), Fritz Zwicky (1898--1974) (author) arXiv, 2017, Nov06, 20 pages: Research: Historic paper by Fritz Zwicky (1898--1974) on dark matter (dunkle materie) in the Coma Cluster translated into English.
See galaxy_cluster_coma.html.
See p. 9--10 for comments on the Coma Cluster with Zwicky's application of the virial theorem K=-(1/2)V_gravity to show that the Coma Cluster has ∼ 400 more dark matter (dunkle materie) than luminous matter. Zwicky's estimate was too large by a factor of ∼ 40. So it is hard to call his work a discovery of dark matter. But it is evidence for discovery.
Keywords: Coma Cluster, cosmological redshift, cosmology, dark matter, Fritz Zwicky (1898--1974), virial theorem K=-(1/2)V_gravity, etc.
1970s: Vera Rubin (1928--2016) et al. showed the galaxy rotation curves did not fall off as expected from the luminous matter: i.e., stars and interstellar medium (ISM) which is only ∼ 10% of stars. The galaxy rotation curves typically plateaued with typical velocity 200 km/s implying significantly more matter than luminous matter.
```
        v = sqrt(GM(r)/r) ≅ sqrt(G(4π/3)ρ_ave*r**2)
        which if v is constant implies ρ_ave ∝ 1/r**2 which is cuspy.
        But it is NOT as concentrated as luminous matter.
      
```
The dark matter maybe 5--10 times the luminous matter.
Keywords: dark matter, galaxy rotation curves, Vera Rubin (1928--2016), etc.
See the simulation of galaxy rotation at galaxy_rotation.html.
Galaxy clusters also show evidence for massive dark matter. Typically 5 times luminous matter (see Wikipedia: Dark matter: Galaxy clusters). Galaxy cluster mass can be estimated 3 ways:
1. From the virial theorem K=-(1/2)V_gravity. There are sophisticated ways of doing this (see Wikipedia: virial mass). But the order-of-magnitude way is to use order-of-magitude virial theorem (which drops factors order 1)
```
           (GM/R_σ_max) = σ_max^{2}
          
```
  where σ is the velocity dispersion (standard deviation along the line-of-sight) measured from the Doppler effect σ_max is its maximum value, R_σ_max is the radius from the center along which σ_max occurs (see Wikipedia: Virial theorem: In astrophysics).
2. From X-ray observations of the hot intracluster medium together with the assumption of hydrostatic equilibrium of the intracluster medium.
3. From gravitational lensing: both strong gravitational lensing and weak gravitational lensing. See strong gravitational lensing image.
The CMB angular power spectrum shows the signature of many cosmological effects including dark matter particularly in the 3rd peak. See the angular power spectrum image. The fact that the CMB angular power spect rum can be predicted from Λ-CDM model plus inflation is strong evidence for both those theories. MOND (MOdified Newtonian Dynamics) is disfavored by the angular power spectrum image (see Wikipedia: Dark matter: Cosmic microwave background). But MOND is the Dracula theory: it always rises from the dead.
Structure formation (AKA large-scale structure formation) requires dark matter, specifically cold dark matter (CDM), to get the large-scale structure of the universe. Knowing this requires computer simulations. Originally, one just N-body simulation which just include cold dark matter (CDM): i.e., matter that only interacts gravitationally. They did a good 1st order job. Nowadays baryonic matter and a lot of sophistication (e.g., AGN feedback and supernova) is included to model galaxies realistically.
See large-scale structure image, large-scale structure animation, and Large-Scale structure of the universe videos.
Then there is the Bullet Cluster which is naturally explained by dark matter, but NOT MOND.
But what is dark matter?
Well about 20 % is baryonic matter: i.e., ordinary matter: protons, neutrons, and electrons. Only about 1/10 of this is in stars. The rest is baryonic dark matter which overwhelmingly is intergalactic medium (IGM), much of which is warm-hot intergalactic medium (WHIM). For a long time there was a problem finding enough of this: this was the missing baryon problem (AKA missing mass problem). But now it's accounted for.
Why can't all the dark matter be baryonic matter? Big Bang nucleosynthesis (BBN) forbids this. BBN fits very well for the primordial cosmic composition which just consists of the light elements. It can't produce more baryonic matter than about 20 % of the matter without spoiling that fit. See big_bang_nucleosynthesis.html.
See cosmos_energy_pie_chart.html for the mass-energy contents of the observable universe in the Λ-CDM model.
Wikipedia: Neutrino: Wikipedia: Neutrino: Mass, KATRIN
Wikipedia: Cross section: see first figure.
barn = 10**(-28) m**2 = 100 fm**2: Wikipedia: Barn (unit): Wikipedia: Barn (unit): Commonly used prefixed versions. American idiom: "couldn't hit the broad side of a barn."
Thomson cross section σ = 0.66524587321(60) barns (see NIST:Fundamental Physical Constants --- Complete Listing. See also Thomson scattering.
weakly interacting massive particles (WIMPS), WIMP miracle, supersymmetry, Wikipedia: Weakly interacting massive particles (WIMPs): Wikipedia: WIMPs as dark matter, Wikipedia: Indirect detection, Wikipedia: Direct detection, Wikipedia: DAMA/LIBRA, Images: WIMPs.
Wikipedia: Axions, Wikipedia: Axions: Cosmological implications.
Wikipedia: Massive Compact Halo Objects (MACHOs).
Wikipedia: Primordial black hole: There has been a lot of interest in them lately as dark matter and as seeds for some of the supermassive black holes. I think they have to be massive enough to account for dark matter and still be rare enough NOT be detected as MACHOs. However, Banik et al. 2018 argue that WIMPs help form the massive Population III stars that provide the seeds for supermassive black holes---fascinating as would say Spock.
Wikipedia: MOdified Newtonian Dynamics (MOND): The Devil's advocate---or Dracula: the undead theory.
Wikipedia: Bullet Cluster.
Wikipedia: Core-cusp problem.