Physical origin and magnitude of the cosmological constant

Explain the physical origin of the observed small positive cosmological constant Λ in the Einstein field equations for cosmology, and reconcile its measured magnitude with quantum field theoretic predictions of vacuum energy density that are many orders of magnitude larger. Identify a mechanism that yields an effective stress–energy component with equation of state w = −1 and the observed size.

Background

Within the discussion of cosmology, the text presents two perspectives on the cosmological constant: as a geometric term that renders vacuum spacetimes maximally symmetric (de Sitter/anti–de Sitter), and as an effective matter–energy component with stress–energy tensor T_Λ^μν = −Λ g^μν and equation of state w = −1. While observations indicate a small positive value for Λ consistent with late-time cosmic acceleration, quantum field theory predicts a vacuum energy density that is vastly larger than what is measured, leading to a stark discrepancy known as the cosmological constant problem.

The author explicitly notes that, despite the plausibility of attributing Λ to zero-point vacuum energy, current theoretical calculations do not match observations, leaving the fundamental physical origin and precise magnitude of Λ unresolved. This motivates a concrete open problem to explain the source and correct scale of Λ in the context of general relativity and quantum field theory.