Maximally Symmetric Spin-Two Bitensors on $S^3$ and $H^3$

Abstract

The transverse traceless spin-two tensor harmonics on $S^3$ and $H^3$ may be denoted by $T^{(kl)}{}_{ab}$. The index $k$ labels the (degenerate) eigenvalues of the Laplacian $\square$ and $l$ the other indices. We compute the bitensor ${\sum }_l{T}^{(kl)}{}_{ab}(x)T^{(kl)}{}_{a^{\prime }{b}^{\prime }}(x^{\prime }{)}^{\ast }$ where $x,x^{\prime }$ are distinct points on a sphere or hyperboloid of unit radius. These quantities may be used to find the correlation function of a stochastic background of gravitational waves in spatially open or closed Friedman-Robertson-Walker cosmologies.

arXiv comment12 pages, RevTeX, uuencoded compressed .tex file, minor typos corrected

References in corpus (1)

• Green's function for gravitational waves in FRW spacetimes

Cited by in corpus (12)

• Brane New World
• Quantum Fluctuations, Decoherence of the Mean Field, and Structure Formation in the Early Universe
• A Holographic Framework for Eternal Inflation
• Gravitational Waves in Open de Sitter Space
• Emergent Cosmology Revisited
• Primordial Gravitational Waves From Open Inflation
• Bubble fluctuations in $\Omega <1$ inflation
• Gravity Waves from Instantons
• On cosmic hair and "de Sitter breaking" in linearized quantum gravity
• Gupta-Bleuler quantization for linearized gravity in de Sitter spacetime
• `Hidden' symmetry of linearized gravity in de Sitter space
• Graviton and Scalar Two-Point Functions in a CDL Background for General Dimensions