Curvature, zero modes and quantum statistics

We explore an intriguing connection between the Fermi–Dirac and Bose–Einstein statistics and the thermal baths obtained from a vacuum radiation of coherent states of zero modes in a second quantized (many-particle) theory on the compact O(3) and noncompact O(2, 1) isometry subgroups of the de Sitter and anti-de Sitter spaces, respectively. The high frequency limit is retrieved as a (zero-curvature) group contraction to the Newton–Hooke (harmonic oscillator) group. We also make some comments on the vacuum energy density and the cosmological constant problem.