The Cosmic Microwave Background Spectrum and a Determination of Fractal
  Space Dimensionality
  The possibility to constrain fractal space dimensionality from Astrophysics
and other areas is briefly reviewed. Assuming such dimensionality to be $3 +
\epsilon$, a limit to $\epsilon$ can be inferred from COBE satellite data. The
available data for the cosmic microwave background radiation spectrum are
fitted by a Planck's radiation distribution generalized to non integer space
dimensionality. Our analysis shows that the shape of the CMBR spectrum, which
does not depend on the absolute normalization, is correctly described from this
distribution provided the absolute temperature is equal to 2.726 $\pm$
$0.003\times 10^{-2}$ K and $\epsilon = - (0.957 \pm 0.006) \times 10^{-5}$.
This value for $\epsilon$ is shown to be consistent with what is found on a
very different spatial scale based on a quantum field phenomenon. The
$|\epsilon|$ is interpreted as an upper limit for how much space dimensionality
could have deviated from three. In other words, this is the maximum fluctuation
space dimensionality should have experienced in a spatial and temporal scale
compared to that of the decoupling era.
