Vacuum Polarization in Spatially-flat $N$-dimensional Friedman--Robertson--Walker Spacetimes

Abstract

We investigate the vacuum polarization, φ 2 , 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 ≤ 12. 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 φ 2 for 4 ≤ N ≤ 12 is examined in the exponentially expanding universe, in the power-law and inflationary powerlaw models. In the case of exponential expansion, φ 2 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.

Stress-energy Tensor of the Quantized Massive Fields in Spatially-flat $D$-dimensional Friedmann--Robertson--Walker Spacetimes

“…On the other hand, the semiclassical analysis can teach us a lot about the influence of the quantized fields on the black hole interior and about the tendency of the changes of the background geometry as the singularity is approached. Of course, from the point of view of the present work, the most important are the results obtained in cosmology (see e.g., Refs [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] and the references cited therein) and in the black hole interiors [28][29][30][31][32][33].…”

“…Note that the knowledge of Ω k is sufficient to construct the vacuum polarization [27]. Indeed, since…”

“…First, observe that on the general ground, the energy density of the massive quantum field has the following form [27]…”

“…One of the most versatile approaches in the quantum field theory in curved background is the adiabatic regularization [15][16][17][18][19][20][24][25][26][27] (see also [35][36][37]). The adiabatic calculations are based on the higher-order WKB approximation to the mode functions and their derivatives and subsequent integration (summation) of the functions thus constructed.…”

Vacuum Polarization of Massive Fields in the Spacetime of the Higher-dimensional Black Holes

“…of distorted black holes [19,20], in the spacetimes of dimension higher (or smaller) than 4 [21][22][23][24][25][26][27][28][29][30][31].…”