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Quantum-to-classical transition of primordial cosmological perturbations in de Broglie-Bohm quantum theory: The bouncing scenario

Nelson Pinto-Neto and Grasiele Santos

Ward Struyve

  • ICRA-Centro Brasileiro de Pesquisas Físicas–CBPF, rua Xavier Sigaud, 150, Urca, CEP22290-180 Rio de Janeiro, Brazil

  • Departments of Mathematics and Philosophy, Rutgers University, Hill Center, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019, USA

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Phys. Rev. D 89, 023517 – Published 14 January, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.023517

Abstract

In a previous work we have exhibited a clear description of the quantum-to-classical transition of cosmological quantum fluctuations in the inflationary scenario using the de Broglie–Bohm quantum theory. These fluctuations are believed to seed the small inhomogeneities, which are then responsible for the formation of large scale structures. In this work we show that using the de Broglie–Bohm theory, it is also possible to describe the quantum-to-classical transition of primordial perturbations which takes place around a bouncing phase, even if the latter is caused by quantum effects due to the quantization of the background geometry.

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  30. In fact, as A1 and A2 depend on k, this assertion depends on the scale we are talking about. For an almost scale-invariant spectrum of cosmological perturbations, the A2 term is larger than the A1 term for all scales of cosmological interest (see Ref. [28]), which enforces the argumentation described below for the transition of quantum-to-classical behavior in bouncing models. Only for very short wavelengths can the A1 term be bigger than A2.

  31. We added the subscript q in the equation of state parameter wq of the fluid dominating the bounce to distinguish it from the equation of state parameter w of the dust fluid (like dark matter) which dominated the Universe at the beginning of the contracting phase, when the Universe was very large. While w≈0 (which leads to an almost scale-invariant spectrum—which is observed—for wavelengths that become longer than the curvature scale during the contracting phase [28]), we have that wq is of the order of one. For example, in the case of radiation wq≈1/3 or in the case of stiff matter wq≈1.

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Phys. Rev. D 89, 023517– Published 14 January, 2014
  • Received 16 October 2013

© 2014 American Physical Society

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