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Zbl 1228.83116
Barrow, John D.; Shaw, Douglas J.
The value of the cosmological constant. (English)
[J] Gen. Relativ. Gravitation 43, No. 10, 2555-2560 (2011). ISSN 0001-7701; ISSN 1572-9532/e

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.

MSC 2000:: *83F05 Relativistic cosmology
85A40 Nonrelativistic cosmology
83C55 Hydrodynamics (general relativity)
83C05 Einstein's equations
83C45 Quantization of the gravitational field
81S40 Path integrals in quantum mechanics

Keywords: cosmology; cosmological constant; dark energy

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Zentralblatt MATH Berlin [Germany]