Abstract
What has been shown in this talk is that the graviton propagator in de Sitter space is OK. If one makes a bad choice of gauge (-fixing term) then the propagator is infra-red divergent. However this is not a problem. You can either make a better choice of gauge (of which there are an infinite number), for which the propagator is completely, finite, or else you can go right ahead and use the infra-red divergent one. We demonstrated that it doesn't matter. Gauge-invariance is the over-riding principle, and it ensures that even if the propagator has an infra-red divergence, the physical scattering amplitudes are finite.
A more detailed discussion of these points can also be found in an earlier published paper |20|. The complete closed form for the graviton propagator with ε = ½ has also been found |22|. Finally a closed form in the de Sitter -non-invariant gauge (1.1) has been recently obtained |26|. This form applies to any spatially-flat Robertson-Walker model.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation (Freedman, San Francisco, 1973) p. 410.
I. Antoniadis, J. Iliopoulos, T.A. Tomaras, Nucl.Phys. B261 (1985) 157.
I. Antoniadis and N.C. Tsamis, Phys.Lett. 144B (1984) 55.
E. Baum, Phys.Lett. 133B (1983) 185.
G. Gibbons, S.W. Hawking and S.T.C. Siklos, The Very Early Universe, Proceedings of the Nuffield Workshop (Cambridge UP, 1983).
R. Brandenburger, Rev.Mod.Phys. 57 (1985) 1.
B. deWit and R. Gastmans, Nucl.Phys. B128 (1985) 1.
N.P. Myhrvold, Phys.Lett. 132B (1983) 308.
N.P. Myhrvold, Phys.Rev. D28 (1983) 2439.
E. Mottola, Phys.Rev. D31 (1985) 754.
E. Mottola, Phys.Rev. D33 (1986) 1616.
E. Mottola, NSF-ITP 85-33 preprint UCSB. E. Mottola and P. Mazur, NSF-ITP 85-153 preprint UCSB.
S. Wada and T. Azuma, Phys.Lett. 132B (1983) 313.
P. Anderson, University of Florida at Gainesville preprint, 1985.
Gary T. Horowitz, Phys.Rev. D21 (1980) 1445.
G.W. Gibbons and S.W. Hawking, Phys.Rev. D15 (1977) 2738.
B. Allen, Ann.Phys. 161 (1985) 152.
B. Allen, Nucl.Phys. B226 (1983) 228.
S.W. Hawking and G.F.R. Ellis, The Large Scale Structure of Spacetime (Cambridge UP, 1980).
O. Nachtmann, Commun.Math.Phys. 6 (1967) 1.
N.A. Chernikov and E.A. Tagirov, Ann.Inst. Henri Poincaré IX (1968) 109.
J. Géhéniau and Ch. Schomblond, Bull.Cl.Sci., V.Ser.Acad.R.Belg. 54 (1968) 1147.
E.A. Tagirov, Ann.Phys. 76 (1973) 561.
P. Candelas and D.J. Raine, Phys.Rev. D12 (1975) 965.
Ch. Schomblond and P. Spindel, Ann.Inst. Henri Poincaré XXV (1976) 67.
T.S. Bunch and P.C.W. Davies, Proc.Roy.Soc.Lond. A360 (1978) 117.
B. Allen, Phys.Rev. D32 (1985) 3136.
B. Allen and T. Jacobson, Commun.Math.Phys. 103 (1986) 669.
B. Allen and C.A. Lütken, Commun.Math.Phys. 106 (1986) 201.
O. Nachtman in reference 11.
O. Nachtman, Z. Phys. 208 (1968) 113.
O. Nachtman, Sitzungsber. Oesterr.Akad.Wiss.Math.Naturwiss.Kl. 167 (1968) 363.
G.W. Gibbons and M.J. Perry, Proc.R.Soc.Lond. A358 (1978) 467.
I. Antoniadis, J. Iliopoulos and T.N. Tomaras, Phys.Rev.Lett. 56 (1986) 1319.
C. Itzykson and J.B. Zuber, Quantum Field Theory (McGraw-Hill, NY, 1980).
S. Coleman and E.J. Weinberg, Phys.Rev. D7 (1973) 1888.
This of course is the infinitesimal form of the gauge transformation. To generate finite transformations we have to go to higher order in V.
The Fadeev-Popov determinantIhabI does not depend upon hab at one-loop, and thus does not contribute to the tree-level propagator. We have therefore left this Jacobian out of the formula for Gaba′b′.
B. Allen and T. Jacobson in reference 11.
S.M. Christensen and M.J. Duff, Nucl.Phys. B170 (1980) 480.
N.H. Barth and S.M. Christensen, Phys.Rev. D28 (1983) 1876.
B. Allen, Phys. Rev. D34 (1986) 3670.
B. Allen in reference 19.
S.L. Adler, Phys.Rev. D6 (1972) 3445, D8 (1973) 2400.
R. Raczka, N. Limic and J. Nierderle, J.Math.Phys. 7 (1966) 1861, 7 (1966) 2026, 8 (1967) 1079.
G.W. Gibbons and M.J. Perry, Nucl.Phys. B146 (1978) 90.
S.M. Christensen, M. Duff, G.W. Gibbons, and M.J. Perry, Phys.Rev.Lett. 45 (1980)161.
A. Higuchi, Yale Preprint YTP 85-22 (1985).
A. Chodos, E. Meyers, Ann.Phys. (NY) 156 (1984) 412.
M.A. Rubin and C.R. Ordonez, J.Math.Phys. 25 (1984) 2888, 26 (1985) 65.
B. Allen and M. Turyn, The graviton propagator in maximally symmetric spacer, Tufts University preprint (1986).
R. Wald, Phys.Rev. D17 (1978) 1477.
R. Wald, Commun.Math.Phys. 54 (1977) 1.
S.A. Fulling, M. Sweeny and R. Wald, Commun.Math.Phys. 63 (1978) 259.
In fact the mode that we have labeled ø1 is degenerate. There are five such modes with the same eigenvalue. If the four-sphere is X2 1 +... + X2 5 = 1 then the modes ø il are proportional to the i'th coordinate Xi.
The boundary terms can be shown to vanish in the Lorentzian spacetime case-see reference 20.
B. Allen, The graviton propagator in homogeneous and isotropic spacetimes, Tufts University Preprint TUTP 86-14 (1986). (submitted to Nucl. Phys.)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1987 Springer-Verlag
About this paper
Cite this paper
Allen, B. (1987). Gravitons in de sitter space. In: de Vega, H.J., Sánchez, N. (eds) Field Theory, Quantum Gravity and Strings II. Lecture Notes in Physics, vol 280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-17925-9_31
Download citation
DOI: https://doi.org/10.1007/3-540-17925-9_31
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17925-2
Online ISBN: 978-3-540-47934-5
eBook Packages: Springer Book Archive