Image 1 Caption: A diagram of the observable universe illustrating the cosmological principle.
Features:
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 cosmological principle scale ∼ 400 Mpc = 0.4 Gpc 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
cosmological principle scale ∼ 400 Mpc = 0.4 Gpc
(see Wikipedia:
Cosmological principle: Violations of homogeneity).
Also the
cosmic microwave background (CMB)
is isotropic to about 1 part 10**5 which suggests
extreme
homogeneity
and isotropy
for the observable universe
at
recombination era
(cosmic t = 377,770(3200) y after the Big Bang).
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.
The theory of the overall
HOMOGENEITY
and ISOTROPY of the
observable universe
is called the
cosmological principle.
The concept of the
cosmological principle
(as a vastly simplifying assumption)
was introduced in
general relativistic cosmology
by Albert Einstein (1879--1955)
for what we call the
Einstein universe
discovered in 1917.
But Einstein did NOT use
the name cosmological principle.
The name was introduced by
E.A. Milne (1896--1950).
Of course, E.A. Milne (1896--1950)
and other early users of the
cosmological principle
did NOT have modern evidence for it.
For them, it was a vastly simplifying assumption for research in
cosmology.
For more on
E.A. Milne (1896--1950),
see Astronomer file:
e_a_milne.html.