The two-point functions for perturbations to the metric tensor, or "gravitons" are found for vacuum-state maximally symmetric backgrounds of arbitrary dimension n. We use tensor mode functions on the n-sphere and a general gauge-fixing term. The gauge-invariant part of the resulting graviton propagator is isolated, and is fully evaluated for de Sitter spaces in terms of functions of the geodesic separation. The metric perturbations in turn induce fluctuations in the various curvature tensors away from their background values. Coordinate-independent correlation functions for these fluctuations are found here as sums of maximally symmetric bitensors, and physical implications of their behaviors discussed.
- Pub Date:
- Physics: Astronomy and Astrophysics;
- Gauge Invariance;
- Measuring Instruments;