Over what scale must averaging occur for the Cosmological Principle to hold?
Answer
Larger than a few hundred million light-years
The Cosmological Principle is explicitly stated to hold only on large scales because the universe exhibits significant structure on local levels. Locally, matter clusters into galaxies, superclusters, and voids, violating uniformity. Cosmologists only expect the principle of homogeneity and isotropy to apply reliably when averaging over volumes significantly larger than these structures. The text specifies this threshold is generally considered to be larger than a few hundred million light-years, often cited numerically as roughly $250/h$ Megaparsecs (Mpc). Below this scale, local gravitational influences dominate the distribution.
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