Dark Energy and Modified Gravity

TL;DR

The paper surveys explanations for late-time cosmic acceleration within and beyond General Relativity, focusing on the cosmological constant problem and the coincidence problem. It contrasts dark-energy within GR (including quintessence and more general scalar fields) with infrared-modified gravity exemplified by f(R) theories and DGP brane-worlds, detailing theoretical constraints, perturbation theory, and observational tests. It finds that while these modified gravity scenarios yield valuable insights into gravity and structure formation, they encounter significant theoretical and observational hurdles (e.g., solar-system constraints, ghosts, and ISW/growth mismatches), and LCDM remains the most consistent fit to current data. The work emphasizes that the exploration sharpens tests of GR on cosmological scales and guides future observations to distinguish between subtle differences in expansion history and perturbation evolution.

Abstract

Explanations of the late-time cosmic acceleration within the framework of general relativity are plagued by difficulties. General relativistic models are mostly based on a dark energy field with fine-tuned, unnatural properties. There is a great variety of models, but all share one feature in common -- an inability to account for the gravitational properties of the vacuum energy, and a failure to solve the so-called coincidence problem. Two broad alternatives to dark energy have emerged as candidate models: these typically address only the coincidence problem and not the vacuum energy problem. The first is based on general relativity and attempts to describe the acceleration as an effect of inhomogeneity in the universe. If this alternative could be shown to work, then it would provide a dramatic resolution of the coincidence problem; however, a convincing demonstration of viability has not yet emerged. The second alternative is based on infra-red modifications to general relativity, leading to a weakening of gravity on the largest scales and thus to acceleration. Most examples investigated so far are scalar-tensor or brane-world models, and we focus on the simplest candidates of each type: $f(R)$ models and DGP models respectively. Both of these provide a new angle on the problem, but they also face serious difficulties. However, investigation of these models does lead to valuable insights into the properties of gravity and structure formation, and it also leads to new strategies for testing the validity of General Relativity itself on cosmological scales.

Figures (10)

• Figure 1: Observational constraints in the $(\Omega_{m},\Omega_\Lambda)$ plane: joint constraints from supernovae (SNe), baryon acoustic oscillations (BAO) and CMB (from Kowalski:2008ez).
• Figure 3: Left: The ISW potential, $(\Phi-\Psi)/2$, for $f(R)$ models, where the parameter $B_0$ indicates the strength of deviation from general relativity [see Eq. (\ref{['bpara']})]. Right: The large-angle CMB anisotropies for the models of the left figure. (For more details see Song:2007da, where this figure is taken from.)
• Figure 4: The confinement of matter to the brane, while gravity propagates in the bulk (from Cavaglia:2002si).
• Figure 5: The confidence contours for supernova data in the DGP density parameter plane. The blue (solid) contours are for SNLS data, and the brown (dashed) contours are for the Gold data. The red (dotted) curve defines the flat models, the black (dot-dashed) curve defines zero acceleration today, and the shaded region contains models without a big bang. (From mm.)
• Figure 6: Joint constraints [solid thick (blue)] from the SNLS data [solid thin (yellow)], the BAO peak at $z=0.35$ [dotted (green)] and the CMB shift parameter from WMAP3 [dot-dashed (red)]. The left plot show DGP models , the right plot shows LCDM. The thick dashed (black) line represents the flat models, $\Omega_K=0$. (From mm.)