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.