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

Bruce Allen
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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 $\sum_l T^{(kl)}{}_{ab}(x) T^{(kl)}{}_{a'b'}(x')^*$ where $x,x'$ 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.

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Bruce Allen. 1994-11-16. Maximally Symmetric Spin-Two Bitensors on $S^3$ and $H^3$. https://doi.org/10.1103/physrevd.51.5491

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