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Quantum and Statistical Effects in Superspace Cosmology

  • Chapter
Book cover Quantum Mechanics in Curved Space-Time

Part of the book series: NATO ASI Series ((NSSB,volume 230))

Abstract

The general aim of these lectures is twofold:

  1. 1)

    To develop a viewpoint for understanding the kinematics of quantum cosmology in the minisuperspace approximation: i.e., superspace as the space of collective excitation modes of spacetime. Emphasis here is put on the spectrum of the Lifshitz operator in spacetime and that of the Wheeler-DeWitt operator in superspace. Some established theorems on the zero-mode structure and asymptotic distribution of eigenvalues of invariant operators in curved space are invoked.

  2. 2)

    To apply some recent results in quantum field theory in curved spacetime to problems in quantum cosmology. Specifically, the analysis of a) infrared behavior and b) dissipative behavior of quantum fields in curved spacetimes are used to elicit the views that a) minisuperspace cosmology is the infrared limit of quantum gravity, and b) dissipative behavior appears in the minisuperspace modes which can lead to memory lost of the initial conditions.

These lectures expound some personal viewpoints and approaches towards current problems in quantum cosmology presented in a semipedagogical way. They are not reviews. Many results quoted here are also of a preliminary nature.

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Authors and Affiliations

  1. Newman Laboratory of Nuclear Studies, Cornell University, Ithaca, New York, 14853, USA

    B. L. Hu

  2. Department of Physics and Astronomy, University of Maryland, College Park, Maryland, 20742, USA

    B. L. Hu

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Editors and Affiliations

  1. Konstanz University, Konstanz, Federal Republic of Germany

    Jürgen Audretsch

  2. Bologna University, Bologna, Italy

    Venzo de Sabbata

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Dedicated to the martyrs of June 4, 1989, whose sacrifice presages a truly people’ s China, whose unflinching spirit inspires the whole humanity.

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Hu, B.L. (1990). Quantum and Statistical Effects in Superspace Cosmology. In: Audretsch, J., de Sabbata, V. (eds) Quantum Mechanics in Curved Space-Time. NATO ASI Series, vol 230. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3814-1_12

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