Built on

A. Di Tucci, J.-L. Lehners, and L. Sberna, “No-boundary prescriptions in Lorentzian quantum cosmology,” Phys. Rev. D
Original
1911
Earlier work this paper cites.
G. W. Gibbons and S. W. Hawking, “Action Integrals and Partition Functions in Quantum Gravity,” Phys. Rev. D
1977
Earlier work this paper cites.
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1980
Earlier work this paper cites.
J. B. Hartle and S. W. Hawking, “Wave Function of the Universe,” Phys. Rev
1987
Earlier work this paper cites.
J. Louko, “Canonizing the Hartle-hawking Proposal,” Phys. Lett. B
1988
Earlier work this paper cites.
J. J. Halliwell and J. Louko, “Steepest Descent Contours in the Path Integral Approach to Quantum Cosmology. 1. The De Sitter Minisuperspace Model,” Phys. Rev. D
1989
Earlier work this paper cites.
G. W. Lyons, “Complex solutions for the scalar field model of the universe,” Phys. Rev. D
1992
Earlier work this paper cites.

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J. Louko and R. D. Sorkin, “Complex actions in two-dimensional topology change,” Class. Quant. Grav
1997
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J. M. Maldacena, “The Large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys
1998
Cited alongside, same era.
R. Bousso and S. W. Hawking, “Lorentzian condition in quantum gravity,” Phys. Rev. D
1999
Cited alongside, same era.
A. Di Tucci, M. P. Heller, and J.-L. Lehners, “Lessons for quantum cosmology from anti–de Sitter black holes,” Phys. Rev. D
Original
2007
Cited alongside, same era.
J. B. Hartle, S. Hawking, and T. Hertog, “The Classical Universes of the No-Boundary Quantum State,” Phys. Rev. D
Original
2008
Cited alongside, same era.

Then

J. Feldbrugge, J.-L. Lehners, and N. Turok, “No smooth beginning for spacetime,” Phys. Rev. Lett
Original
2017
Later among the works it cites.
S. F. Bramberger, S. Farnsworth, and J.-L. Lehners, “Wavefunction of anisotropic inflationary universes with no-boundary conditions,” Phys. Rev. D
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2017
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J. Feldbrugge, J.-L. Lehners, and N. Turok, “No rescue for the no boundary proposal: Pointers to the future of quantum cosmology,” Phys. Rev. D
Original
2018
Later among the works it cites.
P. Caputa and S. Hirano, “Airy Function and 4d Quantum Gravity,” JHEP
Original
2018
Later among the works it cites.
M. Kontsevich and G. Segal, “Wick Rotation and the Positivity of Energy in Quantum Field Theory,” Quart. J. Math. Oxford Ser

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2021

Allowable complex metrics in minisuperspace quantum cosmology

Lehners, Jean-Luc

Understand

Kontsevich and Segal (K-S) have proposed a criterion to determine which complex metrics should be allowed, based on the requirement that quantum field theories may consistently be defined on these metrics, and Witten has recently suggested that their proposal should also apply to gravity.

We explore this criterion in the context of gravitational path integrals, in simple minisuperspace models, specifically considering de Sitter (dS), no-boundary and Anti-de Sitter (AdS) examples.
These simple examples allow us to gain some understanding of the off-shell structure of gravitational path integrals.
In all cases, we find that the saddle points of the integral lie right at the edge of the allowable domain of metrics, even when the saddle points are complex or Euclidean.

Built on

A. Di Tucci, J.-L. Lehners, and L. Sberna, “No-boundary prescriptions in Lorentzian quantum cosmology,” Phys. Rev. D
Original
1911
Earlier work this paper cites.
G. W. Gibbons and S. W. Hawking, “Action Integrals and Partition Functions in Quantum Gravity,” Phys. Rev. D
1977
Earlier work this paper cites.
S. Weinberg and E. Witten, “Limits on Massless Particles,” Phys. Lett. B
1980
Earlier work this paper cites.
J. B. Hartle and S. W. Hawking, “Wave Function of the Universe,” Phys. Rev
1987
Earlier work this paper cites.
J. Louko, “Canonizing the Hartle-hawking Proposal,” Phys. Lett. B
1988
Earlier work this paper cites.
J. J. Halliwell and J. Louko, “Steepest Descent Contours in the Path Integral Approach to Quantum Cosmology. 1. The De Sitter Minisuperspace Model,” Phys. Rev. D
1989
Earlier work this paper cites.
G. W. Lyons, “Complex solutions for the scalar field model of the universe,” Phys. Rev. D
1992
Earlier work this paper cites.

Similar

J. Louko and R. D. Sorkin, “Complex actions in two-dimensional topology change,” Class. Quant. Grav
1997
Cited alongside, same era.
J. M. Maldacena, “The Large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys
1998
Cited alongside, same era.
R. Bousso and S. W. Hawking, “Lorentzian condition in quantum gravity,” Phys. Rev. D
1999
Cited alongside, same era.
A. Di Tucci, M. P. Heller, and J.-L. Lehners, “Lessons for quantum cosmology from anti–de Sitter black holes,” Phys. Rev. D
Original
2007
Cited alongside, same era.
J. B. Hartle, S. Hawking, and T. Hertog, “The Classical Universes of the No-Boundary Quantum State,” Phys. Rev. D
Original
2008
Cited alongside, same era.