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While general relativity ties together the cosmic expansion history andgrowth history of large scale structure, beyond the standard model these canhave independent behaviors. We derive expressions for cosmologies withidentical growth histories but different expansion histories, or otherdeviations. This provides a relation for isogrowth cosmologies, but alsohighlights in general the need for observations to measure each of the growth,expansion, gravity, and dark matter property histories.

Isogrowth Cosmology (and How to Map the Universe)