The Robustness of Quintessence

TL;DR

The paper assesses the robustness of quintessence models with inverse power-law potentials across non-SUSY, SUSY, and SUGRA frameworks. It demonstrates that the tracking behavior is stable against one-loop quantum corrections in non-SUSY theories and remains robust under curvature corrections in SUSY scenarios, while Kähler corrections can threaten tracking unless mitigated by high-scale physics. It then shows that straightforward SUGRA realizations can introduce negative potentials, motivating models with vanishing superpotential or special Kähler structures, and presents explicit SUGRA constructions, including a toy inverse-power SUGRA model with α ≥ 11, that yield viable late-time acceleration with ω_Q ≈ -0.82 for Ω_m ≈ 0.3. The work highlights the need to embed quintessence in a full high-energy theory to maintain the tracker properties while providing observationally consistent predictions and guiding future model-building in supergravity and string contexts.

Abstract

Recent observations seem to suggest that our Universe is accelerating implying that it is dominated by a fluid whose equation of state is negative. Quintessence is a possible explanation. In particular, the concept of tracking solutions permits to adress the fine-tuning and coincidence problems. We study this proposal in the simplest case of an inverse power potential and investigate its robustness to corrections. We show that quintessence is not affected by the one-loop quantum corrections. In the supersymmetric case where the quintessential potential is motivated by non-perturbative effects in gauge theories, we consider the curvature effects and the Kähler corrections. We find that the curvature effects are negligible while the Kähler corrections modify the early evolution of the quintessence field. Finally we study the supergravity corrections and show that they must be taken into account as $Q\approx m_{\rm Pl}$ at small red-shifts. We discuss simple supergravity models exhibiting the quintessential behaviour. In particular, we propose a model where the scalar potential is given by $V(Q)=\frac{Λ^{4+α}}{Q^α}e^{\fracκ{2}Q^2}$. We argue that the fine-tuning problem can be overcome if $α\ge 11$. This model leads to $ω_Q\approx -0.82$ for $Ω_{\rm m}\approx 0.3$ which is in good agreement with the presently available data.

Figures (7)

• Figure 1: Energy density of radiation, matter and quintessence in function of the redshift starting from equipartition. Dotted line represents radiation, dashed line is matter and the full line is quintessence.
• Figure 2: Equation of state in function of the redshift starting at equipartition.
• Figure 3: Energy density of radiation, matter and quintessence in function of the redshift starting at $Q_{\rm i}\approx 0.2 \times 10^{-4}$.
• Figure 4: Equation of state for quintessense starting at $Q_{\rm i}\approx 0.2 \times 10^{-4}$.
• Figure 5: Energy density in the SUGRA model of quintessence for $\alpha =11$. The solid line is the energy density of quintessence whereas dashed-dotted and the dashed lines are the energy density of radiation and matter respectively. The dotted line is the energy density of quintessence for the potential $V(Q)=\Lambda ^{4+\alpha }Q^{-\alpha }$ for $\alpha =11$. The initial conditions are such that equipartition is realized just after inflation.