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Ordinary matter clumps under gravitational attraction only when it loses energy through radiation. Dark matter supposedly doesn't clump since it can only exchange energy with itself and ordinary matter gravitationally. However, if dark matter is interacting with ordinary matter that is losing energy through radiation, wouldn't the dark matter also lose energy by proxy, causing it to clump? By this reasoning dark matter should be denser where ordinary matter is (or has been) radiating strongly. I.e. did matter clump first, and cause dark matter to clump, or vice-versa?

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