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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 ${{\Omega }}_{\mathrm{k}0}\equiv -k/{a}_{0}^{2}{H}^{2}=-0·0055$, which will be tested by Planck Satellite data. Our theory also creates a new picture of self-consistent quantum cosmological history.
##### MSC:
 83F05 Relativistic cosmology 85A40 Cosmology (astronomy and astrophysics) 83C55 Macroscopic interaction of the gravitational field with matter (general relativity) 83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems) 83C45 Quantization of the gravitational field 81S40 Path integrals in quantum mechanics
##### Keywords:
cosmology; cosmological constant; dark energy
##### References:
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