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$H_0$ tension and the String Swampland

[Abridged] We realize the Agrawal-Obied-Vafa (AOV) swampland proposal of fading dark matter by the model of Salam-Sezgin and its string realization of Cvetic-Gibbons-Pope. The model describes a compactification of 6-dimensional supergravity with a monopole background on a 2-sphere. In 4 dimensions, there are 2 scalar fields, $X$ and $Y $, and the effective potential in the Einstein frame is an exponential with respect to $Y$ times a quadratic polynomial in the field $e^{-X}$. When making the volume of the 2-sphere large, namely for large values of $Y$, there appears a tower of states, which according to the infinite distance swampland conjecture becomes exponentially massless. If the standard model fields are confined on Neveu-Schwarz 5-branes the 6-dimensional gauge couplings are independent of the string dilaton in the string frame, and upon compactification to 4 dimensions the 4-dimensional gauge couplings depend on $X$ (rather than the dilaton $Y$) which is fixed at the minimum of the potential. This avoids direct couplings of the dilaton to matter suppressing extra forces competing with gravity. We show that this set up has the salient features of the AOV models, and ergo can potentially ameliorate the tension between local distance ladder and cosmic microwave background estimates of the Hubble constant $H_0$. Although the AOV proposal does not fully resolve the tension in $H_0$ measurements, it provides a dynamical dark energy model of cosmology that satisfies the de Sitter swampland conjecture. We comment on a viable solution to overcome the tension between low- and high-redshift observations within the AOV background and discuss the implications for the swampland program.