Canonical measure and the flatness of a FRW universe

Abstract

We consider the claim of Hawking and Page that the canonical measure applied to a FRW universe with a massive scalar field can solve the flatness problem regardless of inflation. By considering a general potential we are able to understand how the ambiguity for $\Omega$ found by Page in the $R^2$ theory is present when the potential is bounded from above. We suggests reasons why such potentials are realistic. The ambiguity for the possibility of inflation present in the Gibbons- Hawking- Stewart measure can be resolved by an input from Quantum cosmology. We contrast the resulting measure obtained in this way with those obtained in the more usual approaches to quantum cosmology. The measure agrees with that found from a "classical" signature change.

22 pages , Latex. University of Cape Town, report 94

References in corpus (4)

• Eternal inflation and the initial singularity
• Open and Closed Universes, Initial Singularities and Inflation
• Hamiltonian quantization of General Relativity with the change of signature
• The massive scalar field in a closed Friedmann universe model - new rigorous results

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• Entropic issues in contemporary cosmology
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• Comments on the Canonical Measure in Cosmology
• A measure on the set of compact Friedmann-Lemaitre-Robertson-Walker models