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 and for massive transverse vectors with , where is the dimension of space-time and 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.
REFERENCES
1.
G.
‘t Hooft
and M.
Veltman
, Nucl. Phys. B
44
, 189
(1972
);C. G.
Bollini
and J. J.
Giambiagi
, Nuovo Cimento Soc. Ital. Fis., B
12
, 20
(1972
).2.
F.
Bloch
and A.
Nordsieck
, Phys. Rev.
52
, 54
(1937
).3.
G.
Veneziano
, Nucl. Phys. B
44
, 142
(1972
).4.
N. C.
Tsamis
and R. P.
Woodard
, Ann. Phys. (N.Y.)
238
, 1
(1995
).5.
N. C.
Tsamis
and R. P.
Woodard
, Class. Quantum Grav.
20
, 5205
(2003
);e-print arXiv:astro-ph/0206010.
6.
L. H.
Ford
and L.
Parker
, Phys. Rev. D
16
, 245
(1977
).7.
T. M.
Janssen
, S. P.
Miao
, T.
Prokopec
, and R. P.
Woodard
, Class. Quantum Grav.
25
, 245013
(2008
);e-print arXiv:0808.2449.
8.
T. S.
Bunch
and P. C. W.
Davies
, Proc. R. Soc. London, Ser. A
357
, 381
(1977
).9.
T.
Janssen
and T.
Prokopec
, Ann. Phys. (N.Y.)
325
, 948
(2010
);10.
A.
Vilenkin
, Nucl. Phys. B
226
, 527
(1983
).11.
N. C.
Tsamis
and R. P.
Woodard
, Class. Quantum Grav.
11
, 2969
(1994
).12.
T. M.
Janssen
, S. P.
Miao
, T.
Prokopec
, and R. P.
Woodard
, J. Cosmol. Astropart. Phys.
05
(2009
), 003
;e-print arXiv:0904.1151.
13.
B.
Allen
and A.
Folacci
, Phys. Rev. D
35
, 3771
(1987
).14.
E. O.
Kahya
and R. P.
Woodard
, Phys. Rev. D
72
, 104001
(2005
);e-print arXiv:gr-qc/0508015.
15.
16.
e-print arXiv:astro-ph/0205331;
T.
Prokopec
, O.
Tornkvist
, and R. P.
Woodard
, Ann. Phys. (N.Y.)
303
, 251
(2003
);e-print arXiv:gr-qc/0205130.
17.
T.
Prokopec
and R. P.
Woodard
, J. High Energy Phys.
10
(2003
), 059
;e-print arXiv:astro-ph/0309593.
18.
E. O.
Kahya
and R. P.
Woodard
, Phys. Rev. D
74
, 084012
(2006
);e-print arXiv:gr-qc/0608049.
19.
V. K.
Onemli
and R. P.
Woodard
, Class. Quantum Grav.
19
, 4607
(2002
);e-print arXiv:gr-qc/0204065;
V. K.
Onemli
and R. P.
Woodard
, Phys. Rev. D
70
, 107301
(2004
);e-print arXiv:gr-qc/0406098.
20.
T.
Brunier
, V. K.
Onemli
, and R. P.
Woodard
, Class. Quantum Grav.
22
, 59
(2005
);e-print arXiv:gr-qc/0408080.
21.
T.
Prokopec
, N. C.
Tsamis
, and R. P.
Woodard
, Class. Quantum Grav.
24
, 201
(2007
);e-print arXiv:gr-qc/0607094.
22.
T.
Prokopec
, N. C.
Tsamis
, and R. P.
Woodard
, Ann. Phys. (N.Y.)
323
, 1324
(2008
);e-print arXiv:0707.0847;
T.
Prokopec
, N. C.
Tsamis
, and R. P.
Woodard
,Phys. Rev. D
78
, 043523
(2008
);e-print arXiv:0802.3673.
23.
24.
N. C.
Tsamis
and R. P.
Woodard
, Phys. Lett. B
292
, 269
(1992
);N. C.
Tsamis
and R. P.
Woodard
, Phys. Rev. D
54
, 2621
(1996
);e-print arXiv:hep-ph/9602317.
25.
N. C.
Tsamis
and R. P.
Woodard
, Ann. Phys. (N.Y.)
321
, 875
(2006
);e-print arXiv:gr-qc/0506056.
26.
S. P.
Miao
and R. P.
Woodard
, Class. Quantum Grav.
23
, 1721
(2006
);e-print arXiv:gr-qc/0511140.
27.
E. O.
Kahya
and R. P.
Woodard
, Phys. Rev. D
76
, 124005
(2007
);e-print arXiv:0709.0536.
28.
E. O.
Kahya
and V. K.
Onemli
, Phys. Rev. D
76
, 043512
(2007
);e-print arXiv:gr-qc/0612026.
29.
S. P.
Miao
and R. P.
Woodard
, Phys. Rev. D
74
, 044019
(2006
);e-print arXiv:gr-qc/0602110.
30.
A.
Vilenkin
and L. H.
Ford
, Phys. Rev. D
26
, 1231
(1982
);31.
S. P.
Miao
, N. C.
Tsamis
, and R. P.
Woodard
, J. Math. Phys.
50
, 122502
(2009
);e-print arXiv:0907.4930.
32.
B.
Allen
and T.
Jacobson
, Commun. Math. Phys.
103
, 669
(1986
).33.
N. C.
Tsamis
and R. P.
Woodard
, J. Math. Phys.
48
, 052306
(2007
);e-print arXiv:gr-qc/0608069.
34.
A.
Folacci
, Phys. Rev. D
46
, 2553
(1992
);e-print arXiv:0911.2064;
A.
Folacci
, Phys. Rev. D
53
, 3108
(1996
).35.
R. P.
Woodard
, in Deserfest: A Celebration of the Life and Works of Stanley Deser
, edited by J. T.
Liu
, M. J.
Duff
, K. S.
Stelle
, and R. P.
Woodard
(World Scientific
, Hackensack
, 2006
), p. 339
;e-print arXiv:gr-qc/0408002.
36.
37.
B.
Allen
and M.
Turyn
, Nucl. Phys. B
292
, 813
(1987
);S. W.
Hawking
, T.
Hertog
, and N.
Turok
, Phys. Rev. D
62
, 063502
(2000
);e-print arXiv:hep-th/0003016;
A.
Higuchi
and S. S.
Kouris
, Class. Quantum Grav.
18
, 4317
(2001
),e-print arXiv:gr-qc/0107036;
A.
Higuchi
and R. H.
Weeks
, Class. Quantum Grav.
20
, 3006
(2003
);e-print arXiv:gr-qc/0212031.
38.
N. C.
Tsamis
and R. P.
Woodard
, Commun. Math. Phys.
162
, 217
(1994
).39.
G.
Kleppe
, Phys. Lett. B
317
, 305
(1993
).40.
I.
Antoniadis
and E.
Mottola
, J. Math. Phys.
32
, 1037
(1991
).41.
A.
Higuchi
and Y. C.
Lee
, Phys. Rev. D
78
, 084031
(2008
);e-print arXiv:0808.0642;
M.
Faizal
and A.
Higuchi
, Phys. Rev. D
78
, 067502
(2008
);e-print arXiv:0806.3735.
© 2010 American Institute of Physics.
2010
American Institute of Physics
You do not currently have access to this content.