Dynamics of dark energy

TL;DR

This review surveys the landscape of dark energy models, contrasting a pure cosmological constant with a broad array of dynamical scalar-field theories and modified gravity. It develops a unified framework for FRW cosmology, surveys observational evidence from SN Ia, CMB, and LSS, and then delves into detailed dynamical analyses of quintessence, K-essence, tachyon, phantom, dilatonic ghost condensate, and Chaplygin gas. A central theme is the role of scaling and autonomous dynamical systems, including couplings to matter, to understand late-time acceleration and potential transitions to acceleration from past scaling regimes. The work also covers reconstruction methods, perturbation theory, and observational parametrizations of the equation of state, highlighting how data can distinguish Λ from dynamical dark energy and how future observations might reveal genuine dynamics or reinforce the cosmological constant paradigm.

Abstract

In this paper we review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating Universe. In particular we discuss the arguments for and recent progress made towards understanding the nature of dark energy. We review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence, tachyon, phantom and dilatonic models. The importance of cosmological scaling solutions is emphasized when studying the dynamical system of scalar fields including coupled dark energy. We study the evolution of cosmological perturbations allowing us to confront them with the observation of the Cosmic Microwave Background and Large Scale Structure and demonstrate how it is possible in principle to reconstruct the equation of state of dark energy by also using Supernovae Ia observational data. We also discuss in detail the nature of tracking solutions in cosmology, particle physics and braneworld models of dark energy, the nature of possible future singularities, the effect of higher order curvature terms to avoid a Big Rip singularity, and approaches to modifying gravity which leads to a late-time accelerated expansion without recourse to a new form of dark energy.

Figures (26)

• Figure 1: Luminosity distance $d_{L}$ in the units of $H_{0}^{-1}$ for a two component flat universe with a non-relativistic fluid ($w_{m}=0$) and a cosmological constant ($w_{\Lambda}=-1$). We plot $H_{0}d_{L}$ for various values of $\Omega_{\Lambda}^{(0)}$.
• Figure 2: The luminosity distance $H_{0}d_{L}$ (log plot) versus the redshift $z$ for a flat cosmological model. The black points come from the "Gold" data sets by Riess et al.riess2, whereas the red points show the recent data from HST. Three curves show the theoretical values of $H_{0}d_{L}$ for (i) $\Omega_{m}^{(0)}=0$, $\Omega_{\Lambda}^{(0)}=1$, (ii) $\Omega_{m}^{(0)}=0.31$, $\Omega_{\Lambda}^{(0)}=0.69$ and (iii) $\Omega_{m}^{(0)}=1$, $\Omega_{\Lambda}^{(0)}=0$. From Ref. CP05.
• Figure 3: The age of the universe (in units of $H_0^{-1}$) is plotted against $\Omega_m^{(0)}$ for (i) a flat model with $\Omega_m^{(0)}+ \Omega_{\Lambda}^{(0)}=1$ (solid curve) and (ii) a open model (dashed curve). We also show the border $t_0=11$ Gyr coming from the bound of the oldest stellar ages. The region above this border is allowed for consistency. This constraint strongly supports the evidence of dark energy.
• Figure 4: The $\Omega_{m}^{(0)}$-$\Omega_{\Lambda}^{(0)}$ confidence regions constrained from the observations of SN Ia, CMB and galaxy clustering. We also show the expected confidence region from a SNAP satellite for a flat universe with $\Omega_{m}^{(0)}=0.28$. From Ref. aldering.
• Figure 5: The phase plane for $\lambda = 2$ and $\gamma=1$. The scalar field dominated solution (c) is a saddle point at $x = (2/3)^{1/2}$ and $y = (1/3)^{1/2}$. Since the point (d) is a stable spiral in this case, the late-time attractor is the scaling solution with $x=y=(3/8)^{1/2}$. From Ref. CLW.