THE COSMIC MICROWAVE BACKGROUND SPECTRUM AND AN UPPER LIMIT FOR FRACTAL SPACE DIMENSIONALITY

The possibility of constraining fractal space dimensionality from astrophysics and other areas is briefly reviewed. Assuming such dimensionality to be 3 + epsilon, a bound for epsilon can be imposed from data obtained by far-infrared absolute spectrophotometer instrument aboard Cosmic Background Explorer satellite. The available data for the cosmic microwave background radiation ( CMBR) spectrum are fitted by Planck's radiation distribution generalized to noninteger space dimensionality. The present 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 +/- 0.003) x 10(-2) K and epsilon = -(0.957 +/- 0.006) x 10(-5). This result for the last parameter is shown to be similar to what was found on a very different spatial scale based on a quantum phenomenon. The value of vertical bar epsilon vertical bar is interpreted as an upper limit for how much space dimensionality could have deviated from three. In otherwords, this is the maximum fluctuation space dimensionality should have undertaken in a very large spatial and temporal scale compared to that of the decoupling era.