)
and it lies nicely
between the 10 Mpc and 1 Gpc extremes for the transition from structures to patterns.
On size scales less 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 ⪅ 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.
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.
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.
For a bit on the history of the
cosmological principle,
see Astronomer file:
e_a_milne.html.
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.