VACUUM POLARIZATION IN SPATIALLY-FLAT N-DIMENSIONAL FRIEDMAN-ROBERTSON-WALKER SPACETIMES

We investigate the vacuum polarization, h 2 i; of the quantized massive scalar field with a general curvature coupling parameter in the spatially- flat N - dimensional Friedman- Robertson- Walker spacetime with 4 N 1 2. The vacuum polarization is constructed using both adiabatic and Schwinger- DeWitt approaches and the full final results up to N = 7 are explicitly demonstrated. The behavior of h 2 i for 4 N 1 2 is examined in the exponentially expanding universe, in the power- law and inflationary powerlaw models. In the case of exponential expansion, h 2 i is constant and for a given mass it depends solely on the Hubble constant and the curvature coupling parameter. In the power- law models its behavior is more complicated and, generally, decays in time as t n; where n = 2 is the integer part of N = 2. The 2 + 1 - dimensional case is also briefly analyzed. The relevance of the present results to the stress- energy tensor is examined.