Cosmological Principle and its Size Scale

The cosmological principle is the assumption that on a large enough scale the observable universe is homogeneous (same in all places) and isotropic (same in all directions). To explicate further, every cube of space in the observable universe at one instant in cosmic time of large enough size scale (e.g., side length) should have the same average properties (e.g., same density, same distribution of galaxy properties, etc.).

1. Note the cosmological principle is posited for each instant in cosmic time since the Big Bang (a time equal to age of the observable universe = 13.797(23) Gyr (Planck 2018)), but the observable universe does evolve. So the observable universepast---which, of course, we see since the farther out you look, the farther back in cosmic time you see.

2. To further explicate seeing the past of the observable universe: the finite vacuum light speed c = 2.99792458*10**8 m/s: cosmic time means there is a time difference between cosmic present and when a light signal started out toward us. This time difference is called the lookback time. So cosmologists have it over historians: cosmologists can actually see the past---the past elsewhere, NOT the past of where we are in the observable universe: i.e., in the Milky Way in the Local Group in the Virgo Supercluster in the Laniakea Supercluster.

3. How large is the cosmological principle size scale? Current thinking is there is NO single value (Sawala 2025), but rather that as one increases in size from the largest galaxy clusters (which are gravitationally-bound systems with dark matter halo radius ∼ 10 Mpc) to the 1 Gpc scale (Sawala 2025), there is a gradual change from gravitational field ordered structures to random patterns. Galaxy superclusters (size scale ∼ 100 Mpc -- 3 Gpc (which are often a bit in the eye of the beholder) and voids (∼ 10--100 Mpc diameters) fall in the region between ordered structures and random patterns.

4. However, 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)) can be adopted. It has some theoretical justification (Wikipedia: Cosmological principle: Violations of homogeneity) and it lies nicely between the 10 Mpc and 1 Gpc extremes.

5. For a bit on the history of the cosmological principle, see Astronomer file: e_a_milne.html.