General Relativity and Gravitation

, Volume 43, Issue 10, pp 2555–2560 | Cite as

The value of the cosmological constant

  • John D. BarrowEmail author
  • Douglas J. Shaw
Essay Awarded by the Gravity Research Foundation


We make the cosmological constant, Λ, 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 Λ that dominates the wave function of the universe. Our new field equation determines Λ 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.


Cosmology Cosmological constant Dark energy 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.DAMTP, Centre for Mathematical SciencesCambridge UniversityCambridgeUK

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