Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-02-22
J.Math.Phys.51:072503,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
27 pages, no figures, uses LaTeX 2epsilon
Scientific paper
10.1063/1.3448926
Just because the propagator of some field obeys a de Sitter invariant equation does not mean it possesses a de Sitter invariant solution. The classic example is the propagator of a massless, minimally coupled scalar. We show that the same thing happens for massive scalars with $M_S^2 < 0$, and for massive transverse vectors with $M_V^2 \leq -2 (D-1) H^2$, where $D$ is the dimension of spacetime and $H$ is the Hubble parameter. Although all masses in these ranges give infrared divergent mode sums, using dimensional regularization (or any other analytic continuation technique) to define the mode sums leads to the incorrect conclusion that de Sitter invariant solutions exist except at discrete values of the masses.
Miao Shun-Pei
Tsamis Nicholas C.
Woodard Richard P.
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