$H_0$ 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.
