The Swampland, Quintessence and the Vacuum Energy

TL;DR

Problem: Can quintessence with cosmological variations of couplings be realized under the swampland constraint $|\\nabla V|\\ge c\\,V$? Approach: analyze the one-loop Coleman-Weinberg corrections $\\delta V=\\frac{1}{(8\\pi)^2}\\sum_i c_i\\, m_i^4 + ...$ and show that variability in couplings leads to $\\delta V \\sim \\delta \\alpha(\\phi)\\,M^4$, potentially dominating the dark-energy potential. Findings: to realize such models one must accept extreme fine-tuning (or an unprecedented cancellation mechanism) or ensure that $\\phi$ couples only to very light states with $m_i\\lesssim O(H_0)$. Significance: the results challenge the viability of Agrawal et al.'s scenario and highlight a fundamental tension between running dark-sector couplings and vacuum-energy stability in quantum gravity.

Abstract

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.