Quantum Fine-Tuning in Stringy Quintessence Models
  We investigate the extent to which quintessence models for dark energy are
fine-tuned in the context of recent swampland conjectures. In particular, the
issue is whether there is a double fine-tuning in which both $V$ and $|\nabla
V|$ are fine-tuned, or whether there is only a single fine-tuning due to the
relation $|\nabla V|\sim V/M_{pl}$ arising naturally. We find that indeed this
relation arises naturally in simple string compactifications for some scalars,
such as the dilaton and volume modulus, when treated classically. However, we
find that quantum effects can spoil this natural relation, unless the scalar is
conformally coupled to the matter sector. Furthermore, it is well known that
such conformal couplings are generically ruled out by fifth force tests. To
avoid these fifth forces, an interesting proposal is to assume the scalar
(quintessence) only couples to the hidden sector. However, we then find quantum
corrections to $V$ from visible sector Standard Model particles generically
spoil the relation. A possible way out of all these problems is to have the
scalar conformally coupled to a dark sector that is an exact copy of the
Standard Model. This ensures the relation $|\nabla V|\sim V/M_{pl}$ is
maintained naturally even when matter particles run in the loop. However, we
find that quantum corrections from quintessons or gravitons in the loop spoil
the relation if the effective theory has a cutoff greater than $\sim 0.1$ GeV.
