ON THE HEISENBERG INDETERMINACY PRINCIPLE AND THE FORMATION OF STRUCTURE IN THE UNIVERSE

Author:

POLLOCK M. D.12

Affiliation:

1. L.D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Ulitsa Kosygina 2, Moscow 117940, Russia

2. V.A. Steklov Mathematical Institute, Russian Academy of Sciences, Vavilova 42, Moscow 117966, Russia

Abstract

The Heisenberg indeterminacy principle ΔpaΔqa ~ ħ, relating canonically conjugate variables pa and qa, is quantified for the classical action obtained by the reduction of the ten-dimensional heterotic superstring theory to four dimensions, in the mini-superspace (Friedmann space-time) [Formula: see text]. There are two coordinates, α and [Formula: see text], representing position and velocity, respectively, the canonical momenta being [Formula: see text] and [Formula: see text]. In both cases, the result can be expressed as an indeterminacy in the time, (Δt/t)2. The fluctuations connecting position and velocity decrease with time and are always undetectably small, Δt/t ≲ 10−44. But the fluctuations involving velocity and acceleration increase with time, and are evaluated at the time te of equipartition of radiation and matter in the universe. Translated first into a metric fluctuation [Formula: see text], this is equivalent to a Gaussian, scale-invariant spectrum of density fluctuations of magnitude [Formula: see text], where the dimensionless constant B depends only on the compactification scheme. For a Calabi–Yau internal space, the estimate B ≈ 3 implies that ζ ≈ 2 × 10−4, which is sufficient for the creation of galaxies and in approximate agreement with observations of the anisotropy of the cosmic microwave background radiation by COBE and at Tenerife.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Physics and Astronomy,Astronomy and Astrophysics,Nuclear and High Energy Physics

Cited by 20 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On the thermodynamics of the cosmological apparent horizon;The European Physical Journal Plus;2015-11

2. On the application of the field-redefinition theorem to the heterotic superstring theory;The European Physical Journal Plus;2015-05

3. GOLDSTONE FIELDS IN THE SUPERSTRING THEORY;International Journal of Modern Physics D;2008-01

4. ON THE SPECTRUM OF PRIMORDIAL DENSITY FLUCTUATIONS;International Journal of Modern Physics D;2006-09

5. ON THE SUPERSTRING HAMILTONIAN IN THE FRIEDMANN SPACE–TIME;International Journal of Modern Physics D;2006-06

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