The Cosmological Constant

Abstract

This is a review of the physics and cosmology of the cosmological constant. Focusing on recent developments, I present a pedagogical overview of cosmology in the presence of a cosmological constant, observational constraints on its magnitude, and the physics of a small (and potentially nonzero) vacuum energy.

Keywords: cosmological constant; cosmology; vacuum energy.

Figure 1

Dynamics for Ω = Ω_M + Ω_Λ. The arrows indicate the direction of evolution of the parameters in an expanding universe.

Figure 2

Expansion histories for different values of Ω_M and Ω_Λ. From top to bottom, the curves describe (Ω_M, Ω_Λ) = (0.3, 0.7), (0.3, 0.0), (1.0, 0.0), and (4.0, 0.0).

Figure 3

Hubble diagram (distance modulus vs. redshift) from the High-Z Supernova Team [214]. The lines represent predictions from the cosmological models with the specified parameters. The lower plot indicates the difference between observed distance modulus and that predicted in an open-universe model.

Figure 4

Hubble diagram from the Supernova Cosmology Project [197]. The bottom plot shows the number of standard deviations of each point from the best-fit curve.

Figure 5

Constraints in the Ω_M-Ω_Λ plane from the High-Z Supernova Team [214].

Figure 6

Constraints in the Ω_M-Ω_Λ plane from the Supernova Cosmology Project [197].

Figure 7

CMB data (binned) and two theoretical curves: The model with a peak at l ∼ 200 is a flat matter-dominated universe, while the one with a peak at l ∼ 400 is an open matter-dominated universe. From [35].

Figure 8

Constraints in the Ω_M-Ω_Λ plane from the North American flight of the BOOMERANG microwave background balloon experiment. From [171].

Figure 9

Gravitational lens probabilities in a flat universe with Ω_M + Ω_Λ = 1, relative to Ω_M = 1, Ω_Λ = 0, for a source at z = 2.

Figure 10

Limits from supernovae and large-scale structure data on Ω_M and the equation-of-state parameter w_X, in a flat universe dominated by matter and dark energy. Thin contours (on the left) represent limits from CMB and large-scale structure measurements, while thick contours are those from SNe observations; solid lines apply to models with constant w_X, while dashed lines apply to models of dynamical scalar fields. The constraints are portrayed separately on the left, and combined on the right. From [194].

Figure 11

Ω_Λ as a function of the scale factor a, for a universe in which Ω_M0 = 0.3, Ω_Λ0 = 0.7. Indicated are the scale factors corresponding to the Planck era, the electroweak phase transition, and Big Bang Nucleosynthesis.