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The value of the cosmological constant. (English) Zbl 1228.83116
Summary: We make the cosmological constant, $\Lambda $, into a field and restrict the variations of the action with respect to it by causality. This creates an additional Einstein constraint equation. It restricts the solutions of the standard Einstein equations and is the requirement that the cosmological wave function possess a classical limit. When applied to the Friedmann metric it requires that the cosmological constant measured today, $t_{U}$, be ${\Lambda \sim t_{U}^{-2} \sim 10^{-122}}$, as observed. This is the classical value of $\Lambda $ that dominates the wave function of the universe. Our new field equation determines $\Lambda $ in terms of other astronomically measurable quantities. Specifically, it predicts that the spatial curvature parameter of the universe is ${\Omega_{\mathrm{k0}} \equiv -k/a_{0}^{2}H^{2} = -0.0055}$, which will be tested by Planck Satellite data. Our theory also creates a new picture of self-consistent quantum cosmological history.

83F05Relativistic cosmology
85A40Cosmology (astronomy and astrophysics)
83C55Macroscopic interaction of the gravitational field with matter (general relativity)
83C05Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C45Quantization of the gravitational field
81S40Path integrals in quantum mechanics
Full Text: DOI
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