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Cosmology and Quantum Theory

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Quantum Cosmology

Part of the book series: Lecture Notes in Physics ((LNP,volume 835))

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Abstract

Next to flat Minkowski space, the simplest solutions of general relativity are given by isotropic Friedmann–Lemaître–Robertson–Walker (FLRW) universe models. Friedmann–Lemaître–Robertson–Walker (FLRW) model Thanks to spatial isotropy, there is just a single parameter, the scale factor \(a(\hbox {t})\) scale factor determining the spatial scale via the line element

$$ {\text{d}}s^2=-N(t)^2{\text{d}}t^2+a(t)^2{\text{d}}\sigma_k^2 $$
(2.1)

with

$$ {\text{d}}\sigma_k^2={\frac{{\text{d}}r^2}{1-kr^2}}+r^2({\text{d}}\vartheta^2+ \sin^2\vartheta{\text{d}}\varphi^2) .$$
(2.2)

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Notes

  1. 1.

    Rescaling freedom in the closed model is discussed in more detail in Sect. 3.2.1.

  2. 2.

    Alternatively to this Dirac quantization of constraints, one may quantize the reduced phase space of observables \({\fancyscript {O}}\) invariant under gauge transformations \(\delta_{\epsilon}{\fancyscript O}= \{{\fancyscript {O}},\epsilon C\}\) generated by (2.7). problem of time Again, it is difficult to see an evolution picture because in general there is no obvious time parameter among the observables; see Chaps. 12 and 13.

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Authors and Affiliations

  1. Center for Gravitational Physics and Geometry, Pennsylvania State University, 104, Davey Laboratory, University Park, PA, 16802-6300, USA

    Martin Bojowald

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  1. Martin Bojowald
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Bojowald, M. (2011). Cosmology and Quantum Theory. In: Quantum Cosmology. Lecture Notes in Physics, vol 835. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8276-6_2

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  • DOI: https://doi.org/10.1007/978-1-4419-8276-6_2

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