  It has recently been conjectured that string theory does not admit de Sitter
vacua, and that quintessence explains the current epoch of accelerated cosmic
expansion. A proposed, key prediction of this scenario is time-varying
couplings in the dark sector, induced by the evolving quintessence field. We
note that cosmological models with varying couplings suffer from severe
problems with quantum corrections, beyond those shared by all quintessence
models. The vacuum energy depends on all masses and couplings of the theory,
and even small variations of parameters can lead to overwhelmingly large
corrections to the effective potential. We find that quintessence models with
varying parameters can be realised in consistent quantum theories by either: 1)
enforcing exceptional levels of fine-tuning; 2) realising some unknown
mechanism that cancels all undesirable contributions to the effective potential
with unprecedented accuracy; or 3) ensuring that the quintessence field couples
exclusively to very light states, and does not backreact on heavy fields.
