Dark energy in the swampland

In this article, 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 vertical bar Delta pi vertical bar < d similar to O(1) and vertical bar V'vertical bar/V > c similar to 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 less than or similar to 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 idealized 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 similar to 20 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.