The acceleration of the universe and the physics behind it

TL;DR

Classifies dark energy into four classes and shows that background evolution alone cannot identify the underlying physics. The authors argue that perturbations in the Newtonian regime, encapsulated by the functions $(\mathcal{S}_{\rm de},\Delta_{\rm de},F_{\rm m},\Pi_{\rm de})$ and their impact on the Poisson equation, are essential for discrimination. Through explicit DGP (class D) and scalar-tensor (class C) examples, they demonstrate that models with identical $E(z)$ can have different growth histories, motivating joint analyses of expansion, growth, and lensing data as well as local gravity tests. The study thus advocates a staged, complementary observational program and the construction of class-specific target models to robustly test dark-energy physics.

Abstract

Using a general classification of dark enegy models in four classes, we discuss the complementarity of cosmological observations to tackle down the physics beyond the acceleration of our universe. We discuss the tests distinguishing the four classes and then focus on the dynamics of the perturbations in the Newtonian regime. We also exhibit explicitely models that have identical predictions for a subset of observations.

Figures (11)

• Figure 1: Summary of the proposed different classes of models. As discussed in the text, various tests can be designed to distinguish between them. The classes differ according to the kind of new fields and to the way they couple to the metric $g_{\mu\nu}$ and to the standard matter fields. Left column accounts for models where gravitation is described by general relativity while right column models describe a modification of gravity. In the upper line classes, the new fields dominate the matter content of the universe at low redshift. Upper-left models (class A) consist of models in which a new kind of gravitating matter is introduced. In the upper-right models (class C), a light field induces a long-range force so that gravity is not described by a massless spin-2 graviton only. This is the case of scalar-tensor theories of gravity. In this class, Einstein equations are modified and there may be a variation of the fundamental constants. The lower-right models (class D) corresponds to models in which there may exist massive gravitons, such as in some class of braneworld scenarios. These models predict a modification of the Poisson equation on large scales. In the last models (lower-left, class B), the distance duality relation may be violated.
• Figure 2: A possible chain of tests to unveil the nature of dark energy. The goal is to start from the more general hypothesis and to incorporate new data and information one by one in order to check at each step if the hypothesis underlying the equations used in the analysis hold or not. Here $\bar{D}_+$ refers to the growth factor predicted from $w(z)$ assuming general relativity. In particular, it may turn out that a deviation from the Poisson equation may be detected while no deviation from $w=-1$ is established. This would however require to extend the minimal $\Lambda$CDM.
• Figure 3: In the plane $(w,w')$, the filled zone corresponds to quintessence models while the very thin black zone corresponds to DGP models. We have allowed $\Omega_{K0}$ to vary between $-1$ and $1$ and $\Omega_{{\rm m}0}$ between 0 and 1.
• Figure 4: Comparison of the fits of the DGP equation. The solid line corresponds to the fit defined in Eq. (\ref{['fit1']}) while the dashed and dotted lines correspond to the fit defined in Eq. (\ref{['fit2']}) respectively with $z_p=3$ and $z_p=1000$. We have assume $\Omega_{{\rm m}0}=0.3$ and $\Omega_{K0}=0$.
• Figure 5: Comparaison of linear growth factor for the same fits as in Fig. \ref{['fig2']} to the equivalent quintessence model.