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For the first time we calculate quantitatively the influence ofinhomogeneities on the global expansion factor by averaging the Friedmannequation. In the framework of the relativistic second-orderZel'dovich-approximation scheme for irrotational dust we use observationalresults in form of the normalisation constant fixed by the COBE results and wecheck different power spectra, namely for adiabatic CDM, isocurvature CDM, HDM,WDM, Strings and Textures. We find that the influence of the inhomogeneities onthe global expansion factor is very small. So the error in determining the ageof the universe using the Hubble constant in the usual way is negligible. Thisdoes not imply that the effect is negligible for local astronomicalmeasurements of the Hubble constant. Locally the determination of theredshift-distance relation can be strongly influenced by the peculiar velocityfields due to inhomogeneities. Our calculation does not consider such effects,but is contrained to comparing globally homogeneous and averaged inhomogeneousmatter distributions. In addition we relate our work to previous treatments.Comment: 10 pages, version accepted by Phys. Rev.

Age of the universe: Influence of the inhomogeneities on the global expansion factor