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The tension between early and late H0 is revised in the context of axion darkmatter arising naturally from string theoretical integrations of antisymmetrictensor fields over non-trivial cycles. Certain early universe cycles may appearnon-trivial from the perspective of a homology analysis focused on the earlyuniverse, while they may become trivial, when analysed from the perspective ofa homology theory reaching out to lower energies and later times. Suchphenomena can introduce variations in the axion potential that would explainthe observed H0 tension.

H0 tensions in cosmology and axion pseudocycles in the stringy universe