Keine glatter Beginn für die Raumzeit - Vilenkin, Hawking widerlegt?
Verfasst: 16. Jun 2017, 10:08
Die beiden Papiere besagen, dass glatte Anfangsbedingungen wie "no-boundary-proposal" / das "Hartle-Hawking-Instanton" sowie "Inflation /Tunneling aus dem Nichts" nach Vilenkin mathematisch nicht konsistent sind.
https://arxiv.org/abs/1703.02076
Lorentzian Quantum Cosmology
Job Feldbrugge, Jean-Luc Lehners, Neil Turok
(Submitted on 6 Mar 2017)
We argue that the Lorentzian path integral is a better starting point for quantum cosmology than the Euclidean version. In particular, we revisit the mini-superspace calculation of the Feynman path integral for quantum gravity with a positive cosmological constant. Instead of rotating to Euclidean time, we deform the contour of integration over metrics into the complex plane, exploiting Picard-Lefschetz theory to transform the path integral from a conditionally convergent integral into an absolutely convergent one. We show that this procedure unambiguously determines which semiclassical saddle point solutions are relevant to the quantum mechanical amplitude. Imposing "no-boundary" initial conditions, i.e., restricting attention to regular, complex metrics with no initial boundary, we find that the dominant saddle contributes a semiclassical exponential factor which is precisely the inverse of the famous Hartle-Hawking result.
https://arxiv.org/abs/1705.00192
No smooth beginning for spacetime
Job Feldbrugge, Jean-Luc Lehners, Neil Turok
(Submitted on 29 Apr 2017)
We identify a fundamental obstruction to any theory of the beginning of the universe as a semi-classical quantum process, describable using complex, smooth solutions of the classical Einstein equations. The no boundary and tunneling proposals are examples of such theories. We argue that the Lorentzian path integral for quantum cosmology is meaningful and, with the use of Picard-Lefschetz theory, provides a consistent definition of the semi-classical expansion. Framed in this way, the no boundary and tunneling proposals become identified, and the resulting framework is unique. Unfortunately, the Picard-Lefschetz approach shows that the primordial fluctuations are out of control: larger fluctuations receive a higher quantum mechanical weighting. We prove a general theorem to this effect, in a wide class of theories. A semi-classical description of the beginning of the universe as a regular tunneling event thus appears to be untenable.
https://arxiv.org/abs/1703.02076
Lorentzian Quantum Cosmology
Job Feldbrugge, Jean-Luc Lehners, Neil Turok
(Submitted on 6 Mar 2017)
We argue that the Lorentzian path integral is a better starting point for quantum cosmology than the Euclidean version. In particular, we revisit the mini-superspace calculation of the Feynman path integral for quantum gravity with a positive cosmological constant. Instead of rotating to Euclidean time, we deform the contour of integration over metrics into the complex plane, exploiting Picard-Lefschetz theory to transform the path integral from a conditionally convergent integral into an absolutely convergent one. We show that this procedure unambiguously determines which semiclassical saddle point solutions are relevant to the quantum mechanical amplitude. Imposing "no-boundary" initial conditions, i.e., restricting attention to regular, complex metrics with no initial boundary, we find that the dominant saddle contributes a semiclassical exponential factor which is precisely the inverse of the famous Hartle-Hawking result.
https://arxiv.org/abs/1705.00192
No smooth beginning for spacetime
Job Feldbrugge, Jean-Luc Lehners, Neil Turok
(Submitted on 29 Apr 2017)
We identify a fundamental obstruction to any theory of the beginning of the universe as a semi-classical quantum process, describable using complex, smooth solutions of the classical Einstein equations. The no boundary and tunneling proposals are examples of such theories. We argue that the Lorentzian path integral for quantum cosmology is meaningful and, with the use of Picard-Lefschetz theory, provides a consistent definition of the semi-classical expansion. Framed in this way, the no boundary and tunneling proposals become identified, and the resulting framework is unique. Unfortunately, the Picard-Lefschetz approach shows that the primordial fluctuations are out of control: larger fluctuations receive a higher quantum mechanical weighting. We prove a general theorem to this effect, in a wide class of theories. A semi-classical description of the beginning of the universe as a regular tunneling event thus appears to be untenable.