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‘Observational’ Quantum Cosmology

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Book cover Quantum Cosmology - The Supersymmetric Perspective - Vol. 2

Part of the book series: Lecture Notes in Physics ((LNP,volume 804))

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Abstract

Following on the appraisal presented in Chap. 2 of Vol. I, the reader may rightfully be asking: Given the framework of quantum cosmology (QC), where are the boundaries of our knowledge, i.e., what exactly constitutes these limits? What are the best directions to move in, and in particular, what predictions or (falsifiable) tests for the universe can be made using quantum cosmology?

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Notes

  1. 1.

    For the momentum constraints (2.2) at this order, we obtain

    $$h_{ij}{\,^{(3)}\nabla}_k\left({\frac{\updelta{{S_0}}}{\updelta{{h_{ik}}}}}\right)=0\;.$$
    ((2.7))
  2. 2.

    Every solution of (2.8) determines a family of solutions of the classical field equations. Equations (2.7) and (2.8) are equivalent to Einstein’s field equations.

  3. 3.

    Up to this order, the total wave functional thus reads

    $$\varPsi\approx\frac{1}{\mathcal{K}}\exp\left({{\textrm i}} \textbf{M}S_0[h_{ab}]/\hbar \right) {\mathcal{F}} [h_{ab},\phi]\;,$$
    ((2.12))

    where \({\mathcal{F}}\) satisfies the Schrödinger equation.

  4. 4.

    ‘Time’ is thus defined through the chosen solution S 0 of the Hamilton–Jacobi equation. However, \(\boldsymbol{\tau}\) is not a spacetime scalar. Nevertheless, the semi-classical scheme can be implemented with the (functional) Schrödinger equation found by integrating (2.14) over three-dimensional space.

  5. 5.

    Note that \(\breve{\sigma}_2\) is a pure gravitational term.

  6. 6.

    Minisuperspace coordinates \(q^X\) are treated as (semi)classical, while the perturbations constitute quantum mechanical quantitities.

  7. 7.

    Compare with the Born–Oppenheimer approximation, where ignoring the off-diagonal terms amounts to assuming a decoherence process.

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  1. Depto. Fisica Rua Marquês d’Avila e Bolama, Universidade da Beira Interior, 6200-307, Covilhã, Portugal

    Paulo Vargas Moniz

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Moniz, P.V. (2010). ‘Observational’ Quantum Cosmology. In: Quantum Cosmology - The Supersymmetric Perspective - Vol. 2. Lecture Notes in Physics, vol 804. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11570-7_2

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