Dark Energy in the Swampland
  In this Letter, we study the implications of string Swampland criteria for
dark energy in view of ongoing and future cosmological observations. If string
theory should be the ultimate quantum gravity theory, there is evidence that
exact de Sitter solutions with a positive cosmological constant cannot describe
the fate of the late-time universe. Even though cosmological models with dark
energy given by a scalar field $\pi$ evolving in time are not in direct tension
with string theory, they have to satisfy the Swampland criteria
$|\Delta\pi|<d\sim\mathcal{O}(1)$ and $|V'|/V>c\sim\mathcal{O}(1)$, where $V$
is the scalar field potential. In view of the restrictive implications that the
Swampland criteria have on dark energy, we investigate the accuracy needed for
future observations to tightly constrain standard dark-energy models. We find
that current 3-$\sigma$ constraints with $c \lesssim 1.35$ are still well in
agreement with the string Swampland criteria. However, Stage-4 surveys such as
Euclid, LSST and DESI, tightly constraining the equation of state $w(z)$, will
start putting surviving quintessence models into tensions with the string
Swampland criteria by demanding $c<0.4$. We further investigate whether any
idealised futuristic survey will ever be able to give a decisive answer to the
question whether the cosmological constant would be preferred over a
time-evolving dark-energy model within the Swampland criteria. Hypothetical
surveys with a reduction in the uncertainties by a factor of $\sim20$ compared
to Euclid would be necessary to reveal strong tension between quintessence
models obeying the string Swampland criteria and observations by pushing the
allowed values down to $c<0.1$. In view of such perspectives, there will be
fundamental observational limitations with future surveys.
