Abstract
Quantum effective action due to the graviton and the fermion loop is computed in the background spacetime of Robertson-Walker type in higher dimensions. It is shown that in a high temperature limit the statistical factor for fermions (1-2-d) (d=number of space dimension) and the number of helicity states account for most of the differences due to the spin. The method is also applied for a direct product space of Sd1 ×Sd2.

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