Graviton propagator in de Sitter space

B. Allen

doi:10.1103/PhysRevD.34.3670

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Graviton propagator in de Sitter space

B. Allen

Department of Physics, Tufts University, Medford, Massachusetts 02155

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Phys. Rev. D 34, 3670 – Published 15 December, 1986

DOI: https://doi.org/10.1103/PhysRevD.34.3670

Abstract

We consider the graviton propagator in a de Sitter background. The propagator depends upon the choice of a gauge-fixing term $L_{gauge = 1 / 2 F^{2}}$ , and we consider the ‘‘ε gauges’’ with $F^{v}$ = $\nabla_{u}$ ( $h^{uv}$ -ε $g^{uv}$ $h^{σ}$ $_{σ}$ ). We show that the propagator is completely finite and has no infrared divergences provided that ε is not given certain ‘‘exceptional’’ values. It is only for these ‘‘exceptional’’ values of ε that the propagator has an infrared divergence. We then show that in these exceptional cases the divergences are gauge artifacts and are not physical: they make no contribution to any physical tree-level scattering amplitudes. Furthermore, we show that at one-loop order the zero modes which arise (only) if ε is given one of the exceptional values are canceled by the Faddeev-Popov ghosts. There is thus no evidence that the de Sitter background is inconsistent when gravitational fluctuations are considered.

References (15)

I. Antoniadis, J. Iliopoulos and T. N. Tomaras, Phys. Rev. Lett. 56, 1319 (1986).
B. Allen, Tufts University report (unpublished).
L. H. Ford and L. Parker, Phys. Rev. D 16, 245 (1977).
B. Allen, Phys. Rev. D 32, 3136 (1985).
L. H. Ford, Phys. Rev. D 31, 710 (1985).
A. Higuchi, Yale University report, 1985 (unpublished).
B. Allen and T. Jacobson, Commun. Math. Phys. 103, 669 (1986).
G. W. Gibbons and M. J. Perry, Nucl. Phys. B146, 90 (1978).
B. Allen, Nucl. Phys. B226, 228 (1983).
S. M. Christensen and M. J. Duff, Nucl. Phys. B170, [FS1], 480 (1980).
B Allen and M. Turyn (in preparation).
A typical boundary term is of the form int $T_{ab}$ ( ${del}^{b}$ ψ )d $Σ^{a}$ where Σ = $Σ_{in}$ - $Σ_{out}$ is composed of two three-surfaces bounding the interaction region, and psi is a scalar function. Upon further integration by parts, the conservation equation ${del}^{b}$ $T_{ab}$ =0 implies that this boundary term is of the form int $T_{ab}$ d $σ^{ab}$ where σ = partial Σ =0 since ${partial}^{2}$ =0. Thus the boundary terms all vanish.
S. W. Hawking, Commun. Math. Phys. 55, 133 (1977).
Omitted end note.
O. Yasuda, Phys. Lett. 137B, 52 (1984).

[c1] I. Antoniadis, J. Iliopoulos and T. N. Tomaras, Phys. Rev. Lett. 56, 1319 (1986).

[c2] B. Allen, Tufts University report (unpublished).

[c3] L. H. Ford and L. Parker, Phys. Rev. D 16, 245 (1977).

[c4] B. Allen, Phys. Rev. D 32, 3136 (1985).

[c5] L. H. Ford, Phys. Rev. D 31, 710 (1985).

[c6] A. Higuchi, Yale University report, 1985 (unpublished).

[c7] B. Allen and T. Jacobson, Commun. Math. Phys. 103, 669 (1986).

[c8] G. W. Gibbons and M. J. Perry, Nucl. Phys. B146, 90 (1978).

[c9] B. Allen, Nucl. Phys. B226, 228 (1983).

[c10] S. M. Christensen and M. J. Duff, Nucl. Phys. B170, [FS1], 480 (1980).

[c11] B Allen and M. Turyn (in preparation).

[c12] A typical boundary term is of the form int $T_{ab}$ ( ${del}^{b}$ ψ )d $Σ^{a}$ where Σ = $Σ_{in}$ - $Σ_{out}$ is composed of two three-surfaces bounding the interaction region, and psi is a scalar function. Upon further integration by parts, the conservation equation ${del}^{b}$ $T_{ab}$ =0 implies that this boundary term is of the form int $T_{ab}$ d $σ^{ab}$ where σ = partial Σ =0 since ${partial}^{2}$ =0. Thus the boundary terms all vanish.

[c13] S. W. Hawking, Commun. Math. Phys. 55, 133 (1977).

[c14] Omitted end note.

[c15] O. Yasuda, Phys. Lett. 137B, 52 (1984).

Physical Review D

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Graviton propagator in de Sitter space

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