Quintessence: A Review

TL;DR

Quintessence: A Review surveys canonical scalar field models for dark energy, focusing on how the dark energy equation of state $w$ evolves under different potentials. It develops analytic descriptions for three main classes—tracking freezing, scaling freezing, and thawing—and derives growth-rate formulas for matter perturbations to connect background evolution with redshift-space distortions. The review also discusses particle-physics realizations, notably PNGB and extended supergravity models, which can protect the ultra-light quintessence mass from radiative corrections. Current data broadly favor $w$ near $-1$, i.e., $\Lambda$CDM, but thawing models remain viable, and future precise measurements of growth will sharpen tests of dynamical dark energy.

Abstract

Quintessence is a canonical scalar field introduced to explain the late-time cosmic acceleration. The cosmological dynamics of quintessence is reviewed, paying particular attention to the evolution of the dark energy equation of state w. For the field potentials having tracking and thawing properties, the evolution of w can be known analytically in terms of a few model parameters. Using the analytic expression of w, we constrain quintessence models from the observations of supernovae type Ia, cosmic microwave background, and baryon acoustic oscillations. The tracking freezing models are hardly distinguishable from the LCDM model, whereas in thawing models the today's field equation of state is constrained to be w_0<-0.7 (95 % CL). We also derive an analytic formula for the growth rate of matter density perturbations in dynamical dark energy models, which allows a possibility to put further bounds on w from the measurement of redshift-space distortions in the galaxy power spectrum. Finally we review particle physics models of quintessence- such as those motivated by supersymmetric theories. The field potentials of thawing models based on a pseudo-Nambu-Goldstone boson or on extended supergravity theories have a nice property that a tiny mass of quintessence can be protected against radiative corrections.

Figures (3)

• Figure 1: The field equation of state $w$ versus $a$ for the tracker solution. This case corresponds to the inverse power-law potential $V(\phi)=M^5 \phi^{-1}$. The solid curve is derived by solving Eqs. (\ref{['quinw']})-(\ref{['quinlam']}) numerically, whereas other curves show the 1-st, 2-nd, 3-rd order analytic solutions (\ref{['wtracker']}).
• Figure 2: The field equation of state $w$ versus $a$ for the potential (\ref{['doublepo']}) with (a) $\lambda_1=10$, $\lambda_2=0$, (b) $\lambda_1=15$, $\lambda_2=0$, and (c) $\lambda_1=30$, $\lambda_2=0$. The solid curves are the numerically integrated solutions, whereas the dashed curves show the results derived from the parametrization (\ref{['LHpara']}) with $w_p=0$ and $w_f=-1$. Each dashed curve corresponds to (a) $a_t=0.23$, $\tau=0.33$, (b) $a_t=0.17$, $\tau=0.33$, and (c) $a_t=0.11$, $\tau=0.32$.
• Figure 3: The field equation of state $w$ versus $a$ for the potential (\ref{['pngbpo']}) with (a) $f_a/M_{\rm pl}=0.5$, $\phi_i/f_a=0.5$ ($K=1.9$), (b) $f_a/M_{\rm pl}=0.3$, $\phi_i/f_a=0.25$ ($K=2.9$), and (c) $f_a/M_{\rm pl}=0.1$, $\phi_i/f_a=7.6 \times 10^{-4}$ ($K=8.2$). The solid curves correspond to numerically integrated solutions, whereas the bald dashed curves show the results derived from the analytic solution (\ref{['waap']}) with $\Omega_{\phi 0}=0.73$.