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In the first modern cosmological model, Einstein [1] modified his field equation of General Relativity (GR), introducing a "cosmological term" that enabled a solution with time-independent, spatially homogeneous matter density rhom and constant positive space curvature. Although Einstein did not frame it this way, one can view the "cosmological constant" Λ as representing a constant energy density of the vacuum [2], whose repulsive gravitational effect balances the attractive gravity of matter and thereby allows a static solution. After the development of dynamic cosmological models [3, 4] and the discovery of cosmic expansion [5], the cosmological term appeared unnecessary, and Einstein and de Sitter [6] advocated adopting an expanding, homogeneous and isotropic, spatially flat, matter-dominated universe as the default cosmology until observations dictated otherwise. Such a model has matter density equal to the critical density, Ωmrhom / rhoc = 1, and negligible contribution from other energy components [7].

By the mid-1990s, Big Bang cosmology was convincingly established, but the Einstein-de Sitter model was showing numerous cracks, under the combined onslaught of data from the cosmic microwave background (CMB), large scale galaxy clustering, and direct estimates of the matter density, the expansion rate (H0), and the age of the Universe. Introducing a cosmological constant offered a potential resolution of many of these tensions. In the late 1990s, supernova surveys by two independent teams provided direct evidence for accelerating cosmic expansion [8, 9], establishing the cosmological constant model (with Ωm ≈ 0.3, ΩΛ ≈ 0.7) as the preferred alternative to the Ωm = 1 scenario. Shortly thereafter, CMB evidence for a spatially flat universe [10, 11], and thus for Ωtot ≈ 1, cemented the case for cosmic acceleration by firmly eliminating the free-expansion alternative with Ωm ≪ 1 and ΩΛ = 0. Today, the accelerating universe is well established by multiple lines of independent evidence from a tight web of precise cosmological measurements.

As discussed in the Big Bang Cosmology article of this Review (Sec. 19), the scale factor R(t) of a homogeneous and isotropic universe governed by GR grows at an accelerating rate if the pressure p < -1/3 rho. A cosmological constant has rhoΛconst. and pressure pΛ = -rhoΛ (see Eq. 19.10), so it will drive acceleration if it dominates the total energy density. However, acceleration could arise from a more general form of "dark energy" that has negative pressure, typically specified in terms of the equation-of-state-parameter w = p / rho (= -1 for a cosmological constant). Furthermore, the conclusion that acceleration requires a new energy component beyond matter and radiation relies on the assumption that GR is the correct description of gravity on cosmological scales. The title of this article follows the common but inexact usage of "dark energy" as a catch-all term for the origin of cosmic acceleration, regardless of whether it arises from a new form of energy or a modification of GR. Our account here draws on the much longer review of cosmic acceleration by Ref. [12], which provides background explanation and extensive literature references for most of the points in this article, but is less up to date in its description of current empirical constraints.

Below we will use the abbreviation ΛCDM to refer to a model with cold dark matter, a cosmological constant, inflationary initial conditions, and standard radiation and neutrino content. We will use "flat ΛCDM" to further specify a flat universe with Ωtot = 1. We will use wCDM to denote a model with the same assumptions (including flatness) but a free, constant value of w.

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