Dark Matter and Dark Energy

TL;DR

The paper surveys the evidence for dark matter and dark energy in a flat universe, highlighting how rotation curves, cluster dynamics, lensing, and the CMB support a non-baryonic DM component with \\Omega_m \\simeq \\tfrac13\\) and \\Omega_DE \\simeq \\tfrac23\\. It discusses the successes of CDM on large scales alongside persistent small-scale tensions, such as the substructure and cuspy-core problems, and notes MOND as an alternative with limited relativistic support. The dark energy discussion centers on the cosmological constant problem, anthropic considerations, and a range of dynamical models (Quintessence, Braneworld, Chaplygin gas, Phantom), as well as model-independent reconstruction via the Hubble parameter and the Statefinder diagnostic, to distinguish LCDM from rival scenarios. The work connects observational constraints from Type Ia supernovae, CMB, and large-scale structure to the evolution of the equation of state and the cosmic fate, emphasizing the need for future data and probes to resolve whether the acceleration is driven by a true cosmological constant or evolving dark energy with profound implications for fundamental physics.

Abstract

I briefly review our current understanding of dark matter and dark energy. The first part of this paper focusses on issues pertaining to dark matter including observational evidence for its existence, current constraints and the `abundance of substructure' and `cuspy core' issues which arise in CDM. I also briefly describe MOND. The second part of this review focusses on dark energy. In this part I discuss the significance of the cosmological constant problem which leads to a predicted value of the cosmological constant which is almost $10^{123}$ times larger than the observed value $\la/8πG \simeq 10^{-47}$GeV$^4$. Setting $\la$ to this small value ensures that the acceleration of the universe is a fairly recent phenomenon giving rise to the `cosmic coincidence' conundrum according to which we live during a special epoch when the density in matter and $\la$ are almost equal. Anthropic arguments are briefly discussed but more emphasis is placed upon dynamical dark energy models in which the equation of state is time dependent. These include Quintessence, Braneworld models, Chaplygin gas and Phantom energy. Model independent methods to determine the cosmic equation of state and the Statefinder diagnostic are also discussed. The Statefinder has the attractive property $\atridot/a H^3 = 1 $ for LCDM, which is helpful for differentiating between LCDM and rival dark energy models. The review ends with a brief discussion of the fate of the universe in dark energy models.

Figures (11)

• Figure 1: The observed rotation curve of the dwarf spiral galaxy M33 extends considerably beyond its optical image (shown superimposed); from Roy dproy.
• Figure 2: The power spectrum inferred from observations of large scale structure, the Lyman$\alpha$ forest, gravitational lensing and the CMB. The solid line shows the power spectrum prediction for a flat scale-invariant LCDM model with $\Omega_m = 0.28$, $\Omega_b/\Omega_m = 0.16$, $h = 0.72$; from Tegmark et al. tegmark03a.
• Figure 3: The Earth's motion around the Sun; from Khalil and Munoz (2001).
• Figure 4: Spontaneous symetry breaking in many field theory models takes the form of the Mexican top hat potential shown above. The dashed line shows the potential before the cosmological constant has been 'renormalized' and the solid line after. (From Sahni and Starobinsky 2000.)
• Figure 5: The luminosity distance $d_L$ (in units of $H_0^{-1}$) is shown as a function of cosmological redshift $z$ for spatially flat cosmological models with $\Omega_m + \Omega_\Lambda = 1$. Heavier lines correspond to larger values of $\Omega_m$. The dashed line shows the luminosity distance in the spatially flat de Sitter universe ($\Omega_\Lambda = 1$). From Sahni and Starobinsky ss00.