Image 1 Caption: A diagram of the observable universe illustrating the cosmological principle.

Features:

1. On large enough scales the mass-energy distribution of the observable universe begins to look uniform or, as astronomers often say, homogeneous (same in all places) and isotropic (same in all directions) (see Wikipedia: Cosmological principle: Violations of homogeneity).

   How large is large enough. There is NO sharply defined size, but it is still useful to have a fiducial cosmological principle size scale and the Yadav scale = 370/h_70 Mpc (where reduced Hubble constant h_70=H_0/(70 km/s/Mpc)) is often adopted. It has some theoretical justification (Wikipedia: Cosmological principle: Violations of homogeneity). For further explication of the Yadav scale = 370/h_70 Mpc, see the below Image 2 Caption.

   Note the comoving radius of the observable universe = 14.25 Gpc = 46.48 Gly (current value) according to the Λ-CDM model (AKA the concordance model) of the observable universe (see Wikipedia: Observable universe). So the Yadav scale = 370/h_70 Mpc is much smaller than the scale of the observable universe.

   Note, however, the largest cosmic structures are ∼ 1 Gpc (see Wikipedia: List of largest cosmic structures). But these may be statistical fluctuations and NOT violations of the Yadav scale = 370/h_70 Mpc (see Wikipedia: Cosmological principle: Violations of homogeneity).

   Also, the cosmic microwave background (CMB, T = 2.72548(57) K (Fixsen 2009)) is isotropic to ∼ 1 part 25000 (Wikipedia: Cosmic microwave background: Features) which suggests extreme homogeneity and isotropy for the observable universe at recombination era (cosmic t = 377,770(3200) y after the Big Bang).

2. The homogeneity on the Yadav scale = 370/h_70 Mpc means that if you take a cube of side length 400 Mpc anywhere in the observable universe (at our instant in cosmic time), its average properties would be nearly the same as any other such cube.

   However, scales less than ∼ 400 Mpc, there are variations in the number and behavior of galaxies, galaxy clusters, galaxy superclusters, and other large scale structures. So cubes of side length < 400 Mpc, do NOT have the same average properties. They have a range of properties.

   

3. Image 2 Caption: E.A. Milne (1896--1950).

   E.A. Milne (1896--1950) introduced the term cosmological principle for one of the basic assumptions of general relativistic cosmology. For more on E.A. Milne (1896--1950), see Astronomer file: e_a_milne.html. However, the assumption itself was adopted by Albert Einstein (1879--1955) in the earliest work in cosmology in 1917.

   Further explication of the cosmological principle is in the insert below (local link / general link: cosmological_principle_scale.html).

   EOF

Images:

1. Credit/Permission: © Andrew Colvin (AKA User:Azcolvin429), 2010 / Creative Commons CC BY-SA 3.0.
   Image link: Wikipedia: File:Observable_Universe_with_Measurements_01.png.
   
2. Credit/Permission: © Subrahmanyan Chandrasekhar (1910--1995), 1939 / Uncertain, but the image is just hotlinked.
   Image link: Edward Arthur Milne (1896-1950): Mathematician, Astrophysicist, Cosmologist.