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I'm not at all invested in the above except as a vague thought experiment but imho...

No theory can match CMB as well as the current theories that add cosmic inflation on an as needed basis in time and space to make CMB observations match perfectly. But cosmic inflation is a completely unknown mechanism (no explanation at the level of particle physics) and it was added specifically to make CMB match perfectly. In some ways i think the current 'we observe CMB to be this so we'll move these free variables to make it match' make CMB non-falsifiable. You could add similar free variables to any theory to make CMB match.



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