Abstract
This work investigates the interplay of the Hubble tension, Early Dark Energy (EDE), and the swampland distance conjecture. The latter predicts a tower of light states for large field excursions, while EDE is a scalar field model to alleviate the Hubble tension which indeed requires Planckian field excursions, but also leads to tensions with large-scale structure (LSS) probes. The authors consider exponentially EDE-dependent masses of dark matter with the distance conjecture constant, which supposedly is a positive constant of O(1), as a free parameter. Using a large set of different catalogs of experiments, fitting also LSS data, a mild tension with the swampland distance conjecture is observed that constrains the constant to be significantly less than one. Modifications of the heuristic EDE potential may resolve this conflict.
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