Natural Quintessence in String Theory

TL;DR

The paper builds a string-theoretic quintessence model by embedding a fibre modulus in an anisotropic LARGE Volume Scenario with two large extra dimensions, yielding a radiatively stable, ultra-light scalar that can drive late-time acceleration. The leading-order decoupling from Standard Model fields ensures fifth-force constraints are avoided, while subleading poly-instanton and loop effects generate a quintessence potential with $V \sim m_{3/2}^4$ and mass $m_{\tau_f}^2 \sim m_{3/2}^2 (m_{3/2}/M_P)^2$. It also explores possible couplings to dark matter, particularly KK states, giving a framework for coupled quintessence with a narrow region of parameter space that can support accelerating solutions. Dynamics analyses show viable late-time acceleration without fine-tuning, though no robust dynamical coincidence solution is found; the model remains compatible with current observations and highlights a concrete string-theoretic route to quintessence.

Abstract

We introduce a natural model of quintessence in string theory where the light rolling scalar is radiatively stable and couples to Standard Model matter with weaker-than- Planckian strength. The model is embedded in an anisotropic type IIB compactification with two exponentially large extra dimensions and TeV-scale gravity. The bulk turns out to be nearly supersymmetric since the scale of the gravitino mass is of the order of the observed value of the cosmological constant. The quintessence field is a modulus parameterising the size of an internal four-cycle which naturally develops a potential of the order (gravitino mass)^4, leading to a small dark energy scale without tunings. The mass of the quintessence field is also radiatively stable since it is protected by supersymmetry in the bulk. Moreover, this light scalar couples to ordinary matter via its mixing with the volume mode. Due to the fact that the quintessence field is a flat direction at leading order, this mixing is very small, resulting in a suppressed coupling to Standard Model particles which avoids stringent fifth-force constraints. On the other hand, if dark matter is realised in terms of Kaluza-Klein states, unsuppressed couplings between dark energy and dark matter can emerge, leading to a scenario of coupled quintessence within string theory. We study the dynamics of quintessence in our set-up, showing that its main features make it compatible with observations.

Figures (4)

• Figure 1: Quintessence potential for the fibre modulus. The dotted line represents the poly-instanton generated potential, the dashed line the loop potential from UV physics and the full line the total potential for the canonically normalised fibre modulus.
• Figure 2: Phase plane evolution of the quintessence dark-matter system. Left: the fibre modulus starts in the loop dominated region of the potential; right: the fibre modulus starts in the poly-instanton dominated region of the potential.
• Figure 3: Phase plane evolution of the quintessence dark-matter system with interaction and $F_{\rm poly}\gg F_{\rm loop}$
• Figure 4: Phase plane evolution of the quintessence dark-matter system with interaction and $F_{\rm poly} \sim 10^3 F_{\rm loop}$