Quantum cosmological Friedman models with an initial singularity

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dc.creatorGerhardt, Claus
dc.date2008-06-11
dc.date2008-10-14
dc.date.accessioned2026-07-07T12:38:39Z
dc.date.available2026-07-07T12:38:39Z
dc.descriptionWe consider the Wheeler-DeWitt equation $Hψ=0$ in a suitable Hilbert space. It turns out that this equation has countably many solutions $ψ_i$ which can be considered as eigenfunctions of a Hamilton operator implicitly defined by $H$. We consider two models, a bounded one, $0<r<r_0$, and an unbounded, $0<r<\un$, which represent different eigenvalue problems. In the bounded model we look for eigenvalues $\Lam_i$, where the $\Lam_i$ are the values of the cosmological constant which we used in the Einstein-Hilbert functional, and in the unbounded model the eigenvalues are given by $(-\Lam_i)^{-\frac {n-1}{n}}$, where $\Lam_i<0$. The $ψ_i$ form a basis of the underlying Hilbert space. All solutions have an initial singularity in $r=0$. Under certain circumstances a smooth transition from big crunch to big bang is possible.
dc.description35 pages, v7: Introduction rewritten and and a comparison with the classical solutions added. This will be the published version
dc.identifierhttps://arxiv.org/abs/0806.1769
dc.identifierhttp://arxiv.org/abs/0806.1769
dc.identifierClass.Quant.Grav.26:015001,2009
dc.identifierdoi:10.1088/0264-9381/26/1/015001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/218832
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleQuantum cosmological Friedman models with an initial singularity
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