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Anderson's localization in a random metric: applications to cosmology

J. C. Flores·M. Bologna
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Abstract

It is considered an equation for the Lyapunov exponent $% γ$ in a random metric for a scalar propagating wave field. At first order in frequency this equation is solved explicitly. The localization length $L_{c}$ (reciprocal of Re($γ$)) is obtained as function of the metric-fluctuation-distance $ΔR$ (function of disorder) and the frequency $ω$ of the wave. Explicitly, low-frequencies propagate longer than high, that is $L_{c}ω^{2}=C^{te}$. Direct applications with cosmological quantities like background radiation microwave ($λ\sim 1/2\times 10^{-3}$ [m]) and the Universe-length (`localization length' $L_{c}\sim 1.6\times 10^{25}$ [m]) permits to evaluate the metric-fluctuations-distance as $ΔR\sim 10^{-35}$ [m], a number at order of the Planck's length.

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J. C. Flores, M. Bologna. 2005-01-05. Anderson's localization in a random metric: applications to cosmology. https://arxiv.org/abs/gr-qc/0501012

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