$H_0$ Tension, Swampland Conjectures and the Epoch of Fading Dark Matter
  Motivated by the swampland dS conjecture, we consider a rolling scalar field
as the source of dark energy. Furthermore, the swampland distance conjecture
suggests that the rolling field will lead at late times to an exponentially
light tower of states. Identifying this tower as residing in the dark sector
suggests a natural coupling of the scalar field to the dark matter, leading to
a continually reducing dark matter mass as the scalar field rolls in the recent
cosmological epoch. The exponent in the distance conjecture, $\tilde{c}$, is
expected to be an $\mathcal{O}(1)$ number. Interestingly, when we include the
local measurement of $H_0$, our model prefers a non-zero value of the coupling
$\tilde{c}$ with a significance of $2.8\sigma$ and a best-fit at $\tilde{c}
\sim 0.3$. Modifying the recent evolution of the universe in this way improves
the fit to data at the $2\sigma$ level compared to $\Lambda$CDM. This
string-inspired model automatically reduces cosmological tensions in the $H_0$
measurement as well as $\sigma_8$.
