Evolving Dark Matter Density from Continuous Black Hole Production: A New Observable Signature and its Relation to the Hubble Tension

The Chern-Simons-Kodama (CSK) topological dark matter framework predicts that rotating black holes produce dark matter continuously throughout cosmic his- tory. A direct consequence is that ΩDM is not a cosmological constant but a function of redshift, ΩDM(z), which increases monotonically from the CMB epoch to today. We derive the evolution equation for ΩDM(z) from the CSK production rate inte- grated over the star formation history, and show that the effective equation of state of the CSK dark matter deviates from w = 0 by δw ∼ 1–2%, with a characteristic peak in the ΩDM evolution at z ∼ 1.3, corresponding to the epoch at which the product of star formation rate and dilution factor is maximized (not the SFR peak itself, which occurs at z ∼ 2). This evolution contributes in the correct direction to alleviate the Hubble tension (Hlocal 0 > HCMB 0 ), providing ∆H0 ∼ 0.5 km s−1 Mpc−1 out of the observed discrepancy of 6.0 km s−1 Mpc−1 . While insufficient to fully resolve the tension without specifying the DM sector normalization constant K, the predicted ΩDM(z) evolution is a falsifiable signature of the CSK mechanism, testable with Euclid weak lensing and DESI BAO measurement