Baryonic effects such as AGN feedback can significantly impact the matter clustering, are harder to model from first principles, and emerge as a severe limiting factor in weak lensing cosmology. To tackle this issue, we propose a generic relation of mapping the observed matter clustering to its counterpart in a dark-matter-only universe. We verify this relation to be accurate at better than 1% level at $k<1h/\mathrm{Mpc}$ and $z\in [0,3]$ in both TNG and Illustris simulations, demonstrating its model independence to the underlying baryonic physics. Implementing this relation in observations will be made possible by the specifically designed cross-correlation statistics and baryon census (ionized diffuse gas through localized fast radio bursts, stellar mass through galaxy surveys, and neutral hydrogen through 21 cm mapping). It is capable of correcting the baryonic effect not only in the matter power spectrum, but also at the field level, as demonstrated by tests on the scattering transform statistics. This approach paves the way for constructing the dark-matter-only counterpart of the observed Universe, establishing an ideal cosmological laboratory for probing the dark universe.

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• Large scale structure of the Universe