## Seminars

### Summer term 2021

### Timeless Quantum Mechanics and the Early Universe

Abstract: We discuss the construction and interpretation of observables in quantum theories with worldline diffeomorphism invariance, in which a preferred or absolute time parameter is absent. These theories are also called time-reparametrization invariant, and they can be seen as mechanical toy models of quantum gravity. The interest in these models stems from the necessity of understanding the so-called problem of time in a theory of quantum gravitation: how can the dynamics of quantum states of matter and geometry be defined in a diffeomorphism-invariant way? What is the relevant space of physical states and which operators act on it? How are the quantum states related to probabilities in the absence of a preferred time? We show that the dynamics can be described in terms of relational observables, which are diffeomorphism-invariant extensions of geometrical objects in analogy to gauge-invariant extensions of noninvariant quantities in the usual gauge (Yang-Mills) theories. We take this analogy seriously and use it as a basis of a method of construction of invariant operators in the quantum theory. Furthermore, we discuss how the notion of a physical propagator may be used to define a unitary evolution in the quantum theory, which is to be understood in terms of a generalized clock, as is the classical theory. We also discuss under which circumstances the above mentioned formalism can be related to the use of conditional probabilities in the quantum theory in a generalization of the well-known Page-Wootters approach. Finally, in the interest of making contact with observations, we also examine how our formalism can be adapted to calculations of quantum-gravitational effects in the early Universe.### Working around the non-normalizability of the Lorentzian NBWF

Abstract: The Lorentzian No-Boundary Wavefunction (NBWF) is presented for a free curvature parameter $k$. The choice of the Starobinsky inflation model to be considered for further analysis is motivated. It is shown that the Einstein frame potential of Starobinsky inflation used with the Lorentzian NBWF renders it non-normalizable. Faced with this obstacle, possible workarounds are suggested and supported by heuristic justifications. The breakdown of one of the aforementioned provision is demonstrated, whereas the other provision yields a reasonable pathway to the ensuing slow-roll analysis. Conclusions are drawn on the utility of the tree-level Lorentzian NBWF as a precursor to (Starobinsky) inflation based on the slow-roll analysis in conjunction with a quantum cosmological consistency condition.Date | Time | Speaker | Topic | Room |
---|---|---|---|---|

Apr 13 | 11:30 | Group discussion | Zoom (with password) | |

Apr 21 | 10:00 |
Leonardo Chataignier (Universität zu Köln; disputation) |
Timeless Quantum Mechanics and the Early Universe | Zoom (with password) |

May 11 | 11:30 | Group members | Group discussion | Zoom (with password) |

May 18 | 11:30 | Atharva Rawte (Universität Bonn) |
Working around the non-normalizability of the Lorentzian NBWF | Zoom (with password) |

June 22 | 11:30 | Anupam Mazumdar (RU Groningen) |
TBA | Zoom (with password) |

## Past seminars

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