2010

The IR stability of de Sitter: Loop corrections to scalar propagators

Marolf, Donald, Morrison, Ian A.

Understand

We compute 1-loop corrections to Lorentz-signature de Sitter-invariant 2-point functions defined by the interacting Euclidean vacuum for massive scalar quantum fields with cubic and quartic interactions.

Our results apply to all masses for which the free Euclidean de Sitter vacuum is well-defined, including values in both the complimentary and the principal series of SO(D,1).
In dimensions where the interactions are renormalizeable we provide absolutely convergent integral representations of the corrections.
These representations suffice to analytically extract the leading behavior of the 2-point functions at large separations and may also be used for numerical computations.

Built on

James B. Hartle, “Watson-Sommerfeld Transformation of Many-Particle Scattering Amplitudes,” Phys. Rev. 134
1964
Earlier work this paper cites.
L. J. Slater, “Generalized Hypergeometric Functions,” Cambridge, Cambridge UP (1966)
1966
Earlier work this paper cites.
O. Nachtmann. “Dynamische Stabilität im de-Sitter-raum,” Osterr. Akad. Wiss., Math.-Naturw. Kl., Abt. II 176:363379 (1968)
1968
Earlier work this paper cites.
I. T. Drummond, “Dimensional Regularization Of Massless Theories In Spherical Space-Time,” Nucl. Phys. B 94
1975
Earlier work this paper cites.
J. B. Hartle and S. W. Hawking, “Path Integral Derivation Of Black Hole Radiance,” Phys. Rev. D 13
1976
Earlier work this paper cites.
L. Durand, P. M. Fishbane and L. M. Simmons Jr., “Expansion formulas and addition theorems for Gegenbauer functions,” Jour. Math. Phys. 17
1976
Earlier work this paper cites.
S. L. Adler, “Massless, Euclidean quantum electrodynamics on the five-dimensional unit hypersphere,” Phys. Rev. D 6
1979
Earlier work this paper cites.
A. A. Starobinsky, “Spectrum of relict gravitational radiation and the early state of the universe,” JETP Lett. 30
1979
Earlier work this paper cites.
J. C. Collins, “Renormalization. An Introduction To Renormalization, The Renormalization Group, And The Operator Product Expansion,” Cambridge, Uk: Univ. Pr. ( 1984) 380p
1984
Earlier work this paper cites.
B. Allen, “Vacuum States In De Sitter Space,” Phys. Rev. D 32
1985
Earlier work this paper cites.

Similar

J. Glimm and A. Jaffe, Quantum Physics
1987
Cited alongside, same era.
J. Glimm and A. Jaffe, Quantum Physics
1987
Cited alongside, same era.
B. Allen and M. Turyn, “AN EVALUATION OF THE GRAVITON PROPAGATOR IN DE SITTER SPACE,” Nucl. Phys. B 292
1987
Cited alongside, same era.
N. Ya. Vilenken, and A. U. Klimyk, “Representations of Lie Groups and Special Functions,” vols 1-3. (Dordrecht: Kluwer Acad. Publ. 1991-1993)
1993
Cited alongside, same era.
N. C. Tsamis and R. P. Woodard, “Relaxing The Cosmological Constant,” Phys. Lett. B 301
1993
Cited alongside, same era.
A. A. Starobinsky and J. Yokoyama, “Equilibrium state of a selfinteracting scalar field in the De Sitter background,” Phys. Rev. D 50
1994
Cited alongside, same era.
R. M. Wald, “Quantum field theory in curved space-time and black hole thermodynamics,” (Chicago, Chicago University Press, 1994)
1994
Cited alongside, same era.
N. C. Tsamis and R. P. Woodard, “Strong infrared effects in quantum gravity,” Annals Phys. 238
1995
Cited alongside, same era.
A. Higuchi, “Symmetric tensor spherical harmonics on the N sphere and their application to the de Sitter group SO(N,1),” J. Math. Phys. 28
2002
Cited alongside, same era.
U. H. Danielsson and M. E. Olsson, “On thermalization in de Sitter space,” JHEP 0403
2004
Cited alongside, same era.
A. M. Polyakov, “Decay of Vacuum Energy,” arXiv:0912.5503 [hep-th]
Original
Cited in the paper.
D. Marolf and I. A. Morrison, “The IR stability of de Sitter QFT,” in preparation
Cited in the paper.

Then

N. C. Tsamis and R. P. Woodard, “Quantum Gravity Slows Inflation,” Nucl. Phys. B 474
2005
Later among the works it cites.
N. Arkani-Hamed, talk at the KITP conference String phenomenology 2006
2006
Later among the works it cites.
E. Mottola, “Particle Creation In De Sitter Space,” Phys. Rev. D 31
2007
Later among the works it cites.
R. Szmytkowski, “Closed forms of the Green’s function and the generalized Green’s function for the Helmholtz operator on the N N -dimensional unit sphere,” J. Phys. A: Math. Theor. 40
2007
Later among the works it cites.
M. Srednicki, “Quantum field theory,” Cambridge, UK: Univ. Pr. (2007) 641 p
2007
Later among the works it cites.
S. B. Giddings and D. Marolf, “A global picture of quantum de Sitter space,” Phys. Rev. D 76
Original
2007
Later among the works it cites.
A. M. Polyakov, “De Sitter Space and Eternity,” Nucl. Phys. B 797
Original
2008
Later among the works it cites.
J. Bros, H. Epstein and U. Moschella, “Lifetime of a massive particle in a de Sitter universe,” JCAP 0802
2008
Later among the works it cites.
E. Alvarez and R. Vidal, “Eternity and the cosmological constant,” JHEP 0910
Original
2009
Later among the works it cites.
A. Higuchi, “Decay of the free-theory vacuum of scalar field theory in de Sitter spacetime in the interaction picture,” Class. Quant. Grav. 26
2009
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…