  It is considered an equation for the Lyapunov exponent $% \gamma $ 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($\gamma $)) is obtained as function of the metric-fluctuation-distance
$\Delta R$ (function of disorder) and the frequency $\omega $ of the wave.
Explicitly, low-frequencies propagate longer than high, that is $L_{c}\omega
^{2}=C^{te}$. Direct applications with cosmological quantities like background
radiation microwave ($\lambda \sim 1/2\times 10^{-3}$ [m]) and the
Universe-length (`localization length' $L_{c}\sim 1.6\times 10^{25}$ [m])
permits to evaluate the metric-fluctuations-distance as $\Delta R\sim 10^{-35}$
[m], a number at order of the Planck's length.
