In the first modern cosmological model, Einstein modified his field equation of General Relativity, introducing a “cosmological term” that enabled a solution with time-independent, spatially homogeneous matter density ρm 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, whose repulsive gravitational effect balances the attractive gravity of matter and thereby allows a static solution.

After the development of dynamic cosmological models and the discovery of cosmic expansion, the cosmological term appeared unnecessary, and Einstein and de Sitter 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, Ωm ≡ ρm/ρc = 1, and negligible contribution from other energy components.

By the mid-1990s, the Einstein-de Sitter model was showing numerous cracks, under the combined onslaught of data from the cosmic microwave background, large-scale galaxy clustering, and direct estimates of the matter density, the expansion rate, and the age of the Universe.

As noted in a number of papers from this time, introducing a cosmological constant offered a potential resolution of many of these tensions, yielding the most empirically successful version of the inflationary cold dark matter scenario. In the late 1990s, supernova surveys by two independent teams provided direct evidence for accelerating cosmic expansion, establishing the cosmological constant model (with Ωm ≈ 0.3, ΩΛ ≈ 0.7) as the preferred alternative to the Ωm = 1 scenario.

Shortly thereafter, cosmic microwave background evidence for a spatially flat universe, 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.

A cosmological constant has ρΛ = constant and pressure pΛ = −ρΛ (see Eq. 22.10), 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/ρ (= −1 for a cosmological constant).

Furthermore, the conclusion that acceleration requires a new energy component beyond matter and radiation relies on the assumption that general relativitiy is the correct description of gravity on cosmological scales.

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