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M. Michel Petrovitch, Sur une manière d’étendre le théorème de la moyenne aux équations différentielles du premier ordre , Mathematische Annalen 54
1901
Earlier work this paper cites.
S.F. Bramberger and J.L. Lehners, Nonsingular bounces catalyzed by dark energy , Phys. Rev. D 99
Original
1901
Earlier work this paper cites.
V.D. Ivashchuk, Regularization by ϵ \epsilon -metric , arXiv:1902.03152
Original
1902
Earlier work this paper cites.
A. Di Tucci and J.L. Lehners, No-Boundary Proposal as a Path Integral with Robin Boundary Conditions , Phys. Rev. Lett. 122
Original
1903
Earlier work this paper cites.
P. Virtanen et al., SciPy 1.0–Fundamental Algorithms for Scientific Computing in Python , Nature Meth. 17
Original
1907
Earlier work this paper cites.
A. Di Tucci, J.L. Lehners and L. Sberna, No-boundary prescriptions in Lorentzian quantum cosmology , Phys. Rev. D 100
Original
1911
Earlier work this paper cites.
R. Penrose, Gravitational collapse and space-time singularities , Phys. Rev. Lett. 14
1965
Earlier work this paper cites.
S. Hawking, The Occurrence of singularities in cosmology. II , Proc. Roy. Soc. Lond. A 295
1966
Earlier work this paper cites.
S. Hawking, The occurrence of singularities in cosmology. III. Causality and singularities , Proc. Roy. Soc. Lond. A 300
1967
Earlier work this paper cites.
S.W. Hawking and R. Penrose, The Singularities of gravitational collapse and cosmology , Proc. Roy. Soc. Lond. A 314
1970
Earlier work this paper cites.
G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity , Phys. Rev. D 15
1977
Earlier work this paper cites.
S.R. Coleman and F. De Luccia, Gravitational Effects on and of Vacuum Decay , Phys. Rev. D 21
1980
Earlier work this paper cites.
S.W. Hawking, The Boundary Conditions of the Universe , Pontif. Acad. Sci. Scr. Varia 48
1982
Earlier work this paper cites.
J.B. Hartle and S.W. Hawking, Wave Function of the Universe , Phys. Rev. D 28
1983
Earlier work this paper cites.
J. Louko, Canonizing the Hartle-hawking Proposal , Phys. Lett. B 202
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 39
1989
Earlier work this paper cites.

Similar

J.J. Halliwell and J.B. Hartle, Integration Contours for the No Boundary Wave Function of the Universe , Phys. Rev. D 41
1990
Cited alongside, same era.
R. Bousso and S.W. Hawking, Pair creation of black holes during inflation , Phys. Rev. D 54
1996
Cited alongside, same era.
J. Louko and R.D. Sorkin, Complex actions in two-dimensional topology change , Class. Quant. Grav. 14
1997
Cited alongside, same era.
C.R. Harris et al., Array programming with NumPy , Nature 585
Original
2006
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 102
Original
2007
Cited alongside, same era.

Then

J. Feldbrugge, J.L. Lehners and N. Turok, Lorentzian Quantum Cosmology , Phys. Rev. D 95
Original
2017
Later among the works it cites.
S.F. Bramberger, T. Hertog, J.L. Lehners and Y. Vreys, Quantum Transitions Through Cosmological Singularities , JCAP 07
Original
2017
Later among the works it cites.
S. Gielen and N. Turok, Quantum propagation across cosmological singularities , Phys. Rev. D 95
Original
2017
Later among the works it cites.
J. Feldbrugge, J.L. Lehners and N. Turok, No smooth beginning for spacetime , Phys. Rev. Lett. 119
Original
2017
Later among the works it cites.
J. Diaz Dorronsoro, J.J. Halliwell, J.B. Hartle, T. Hertog and O. Janssen, Real no-boundary wave function in Lorentzian quantum cosmology , Phys. Rev. D 96

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2022

Uses of Complex Metrics in Cosmology

Jonas, Caroline, Lehners, Jean-Luc, Quintin, Jerome

Understand

Complex metrics are a double-edged sword: they allow one to replace singular spacetimes, such as those containing a big bang, with regular metrics, yet they can also describe unphysical solutions in which quantum transitions may be more probable than ordinary classical evolution.

In the cosmological context, we investigate a criterion proposed by Witten (based on works of Kontsevich & Segal and of Louko & Sorkin) to decide whether a complex metric is allowable or not.
Because of the freedom to deform complex metrics using Cauchy's theorem, deciding whether a metric is allowable in general requires solving a complicated optimisation problem.
We describe a method that allows one to quickly determine the allowability of minisuperspace metrics.

Built on

M. Michel Petrovitch, Sur une manière d’étendre le théorème de la moyenne aux équations différentielles du premier ordre , Mathematische Annalen 54
1901
Earlier work this paper cites.
S.F. Bramberger and J.L. Lehners, Nonsingular bounces catalyzed by dark energy , Phys. Rev. D 99
Original
1901
Earlier work this paper cites.
V.D. Ivashchuk, Regularization by ϵ \epsilon -metric , arXiv:1902.03152
Original
1902
Earlier work this paper cites.
A. Di Tucci and J.L. Lehners, No-Boundary Proposal as a Path Integral with Robin Boundary Conditions , Phys. Rev. Lett. 122
Original
1903
Earlier work this paper cites.
P. Virtanen et al., SciPy 1.0–Fundamental Algorithms for Scientific Computing in Python , Nature Meth. 17
Original
1907
Earlier work this paper cites.
A. Di Tucci, J.L. Lehners and L. Sberna, No-boundary prescriptions in Lorentzian quantum cosmology , Phys. Rev. D 100
Original
1911
Earlier work this paper cites.
R. Penrose, Gravitational collapse and space-time singularities , Phys. Rev. Lett. 14
1965
Earlier work this paper cites.
S. Hawking, The Occurrence of singularities in cosmology. II , Proc. Roy. Soc. Lond. A 295
1966
Earlier work this paper cites.
S. Hawking, The occurrence of singularities in cosmology. III. Causality and singularities , Proc. Roy. Soc. Lond. A 300
1967
Earlier work this paper cites.
S.W. Hawking and R. Penrose, The Singularities of gravitational collapse and cosmology , Proc. Roy. Soc. Lond. A 314
1970
Earlier work this paper cites.
G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity , Phys. Rev. D 15
1977
Earlier work this paper cites.
S.R. Coleman and F. De Luccia, Gravitational Effects on and of Vacuum Decay , Phys. Rev. D 21
1980
Earlier work this paper cites.
S.W. Hawking, The Boundary Conditions of the Universe , Pontif. Acad. Sci. Scr. Varia 48
1982
Earlier work this paper cites.
J.B. Hartle and S.W. Hawking, Wave Function of the Universe , Phys. Rev. D 28
1983
Earlier work this paper cites.
J. Louko, Canonizing the Hartle-hawking Proposal , Phys. Lett. B 202
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 39
1989
Earlier work this paper cites.

Similar

J.J. Halliwell and J.B. Hartle, Integration Contours for the No Boundary Wave Function of the Universe , Phys. Rev. D 41
1990
Cited alongside, same era.
R. Bousso and S.W. Hawking, Pair creation of black holes during inflation , Phys. Rev. D 54
1996
Cited alongside, same era.
J. Louko and R.D. Sorkin, Complex actions in two-dimensional topology change , Class. Quant. Grav. 14
1997
Cited alongside, same era.
C.R. Harris et al., Array programming with NumPy , Nature 585
Original
2006
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 102
Original
2007
Cited alongside, same era.

Then

J. Feldbrugge, J.L. Lehners and N. Turok, Lorentzian Quantum Cosmology , Phys. Rev. D 95
Original
2017
Later among the works it cites.
S.F. Bramberger, T. Hertog, J.L. Lehners and Y. Vreys, Quantum Transitions Through Cosmological Singularities , JCAP 07
Original
2017
Later among the works it cites.
S. Gielen and N. Turok, Quantum propagation across cosmological singularities , Phys. Rev. D 95
Original
2017
Later among the works it cites.
J. Feldbrugge, J.L. Lehners and N. Turok, No smooth beginning for spacetime , Phys. Rev. Lett. 119
Original
2017
Later among the works it cites.
J. Diaz Dorronsoro, J.J. Halliwell, J.B. Hartle, T. Hertog and O. Janssen, Real no-boundary wave function in Lorentzian quantum cosmology , Phys. Rev. D 96

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

H. Ooguri and C. Vafa, On the Geometry of the String Landscape and the Swampland , Nucl. Phys. B 766

2007

Cited alongside, same era.

C.M. Bender, D.C. Brody and D.W. Hook, Quantum effects in classical systems having complex energy , J. Phys. A 41

Original

2008

Cited alongside, same era.

S.W. Hawking and G.F.R. Ellis, The Large Scale Structure of Space-Time , Cambridge Monographs on Mathematical Physics, Cambridge University Press (2, 2011), 10.1017/CBO9780511524646

2011

Cited alongside, same era.

E. Witten, Analytic Continuation Of Chern-Simons Theory , AMS/IP Stud. Adv. Math. 50

Original

2011

Cited alongside, same era.

B. Olson, I. Hashmi, K. Molloy and A. Shehu, Basin hopping as a general and versatile optimization framework for the characterization of biological macromolecules , Advances in Artificial Intelligence 2012

2012

Cited alongside, same era.

N. Turok, On Quantum Tunneling in Real Time , New J. Phys. 16

Original

2014

Cited alongside, same era.

S.F. Bramberger, G. Lavrelashvili and J.L. Lehners, Quantum tunneling from paths in complex time , Phys. Rev. D 94

Original

2016

Cited alongside, same era.

Original

2017