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.).

Further explication of the cosmological principle:

1. 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 universe does look different in the past---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 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.

   Note, cosmologists have an advantage over historians: cosmologists can actually see the past---the past elsewhere, NOT the past of where we are in the local observable universe: i.e., in the Milky Way in the Local Group in the Virgo Supercluster in the Laniakea Supercluster. However, given the cosmological principle, the past elsewhere on average is the same as the past for all locations (including the local observable universe).

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 radii ∼ 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 gravitational field 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 for the transition from structures to patterns.

   On size scales less than of order ∼ Yadav scale = 370/h_70 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 less than of order 370/h_70 Mpc do NOT have the same average properties. They have a range of properties and the cosmological principle does NOT apply to them.

5. 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 1 Gpc extreme for the transition from structures to patterns and Yadav scale = 370/h_70 Mpc are both much smaller than the scale of the observable universe.

6. Note 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). Known since circa 2000, this result has always been strong empirical evidence for the cosmological principle.

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

8. The cosmological principle is, in fact, a basic assumption of Big Bang cosmology and of the Λ-CDM model. So it is satisfying that it has been mostly confirmed observationally until at least circa 2025 (e.g., Sawala et al. 2025). However, it may be violated at some level (e.g., Wikipedia: Cosmological principle: Observations). Whether it will continue to be a fundamental principle of cosmology or be demoted to just a good approximate rule for the observable universe, time will tell.