In this work we provide a link between a nearly vanishing cosmological constant and chiral symmetry. This is accomplished with a modification of General Relativity coupled to a topological field theory, namely BF theory by introducing fermions charged under the BF theory gauge group. We find that the cosmological constant sources a chiral anomaly for the fermions, providing a `technical naturalness explanation for the smallness of the observed cosmological constant. Applied to the early universe, we show that production of fermions during inflation can provide all the dark matter in the universe today, in the form of superheavy dark baryons.
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