| On the Stochastic Quantisation of Quantum Gravity with a second order Langevin equation and its physical predictions for the early cosmology |
| Laurent Baulieu, LPTHE Paris |
| Event Type: HEP Seminar |
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| Time: 2:00 PM - 3:30 PM |
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| Location: 726 Broadway, 940, CCPP Seminar |
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| Abstract: Euclidean quantum gravity might be defined by a stochastic quantisation governed by a second order Langevin equation - NOT by a first order stochastic equation as in standard Parisi Wu formulation -, so that interesting acceleration effects occur in the Langevin process.
The prediction of the stochastic 5d theory of 4d gravity with a (+----) signature is that there will a transition from an oscillating 5d phase that defines quantum gravity toward the classical 4d theory where the Minkowski time has emerged.
The predicted end of the transition, as it can be observed from now and described by standard inflation models, is a 4d diluted Universe filled at the beginning with scattered classical primordial black holes. This framework also suggests a gravitational parton stochastic content for "point-like" particles, defined in the same 5d quantum field theory context as in the primordial cosmology.
The higher order Langevin equation for gravity has a pleasant geometrical writing in the 5d space. It defines a foliation for the evolution of a 4d-Euclidean manifold (each leaf being a Universe frozen at a given value of the stochastic time), ordered by the stochastic time. The viscuous force of the Langevin equation is part of the extrinsic curvature of each leaf and its acceleration force is part of the 5d Riemann tensor. The Langevin drift force is the intrinsic curvature of the leaf. Classical gravity is the limit at infinite stochastic time of the physics in the leaf, which otherwise undergo 5d stochastic time oscillations. The transition between the quantum and classical phases must occur with probability one at a period marked by the exit of the inflation. The use of the stochastic times eludes the constraints brought by the Wheeler deWitt equation in the standard description of quantum gravity. |