General Relativity & Quantum Cosmology

Tensor Models provide one of the calculationally simplest approaches to defining a partition function for random discrete geometries. The continuum limit of these discrete models then provides a background-independent construction of a partition function of continuum geometry, which are candadates for quantum gravity. The blue-print for this approach is provided by the matrix model approach to two-dimensional quantum gravity. The past ten years have seen a lot of progress using (un)colored tensor models to describe state sums if discrete geometries in more than two dimensions. However, so far one has not yet been able to find a continuum limit of these models that corresponds geometries with more than two continuum dimensions. This problem can be studied systematically using exact renormalization group techniques. In this talk I will report on joint work with Astrid Eichhorn, Antonio Perreira, Joseph Ben Geloun, Daniele Oriti, Johannes Lumma, Alicia Castro and Victor Mu\~noz in this direction. In a separate part of the talk I will explain that the renormalization group is not only a tool to help investigating the continuum limit, but that it in fact also provides a stand-alone approach to quantum gravity. In particular, I will show how scaling relations follow from cylidrical consistency relations.

We derive Schwarzian correlation functions using the BF formulation of Jackiw-Teitelboim gravity, where bilocal operators are interpreted as boundary-anchored Wilson lines in the bulk. Crossing Wilson lines are associated with OTO-correlators and give rise to 6j-symbols. We discuss the semi-classical bulk black hole physics contained within the correlation functions.

Extensions including bulk defects related to the other coadjoint orbits are discussed.

Gravity theories naturally allow for edge states generated by non-trivial boundary-condition preserving diffeomorphisms. I present a specific set of boundary conditions inspired by near horizon physics, show that it leads to soft hair excitations of black hole solutions and discuss implications for black hole entropy.

I will discuss an attempt at approaching quantum features of spacetime from a microscopic point of view. In combination with quantum gravity, one can consider a scenario in which spacetime has structure at the level of quantum interactions, and classical spacetime emerges at larger scales. This type of scenario would require entangling interactions, and a reliance on information exchange would have effects on the classical field theory.

The conservation law for the total (orbital plus spin) angular momentum of a Dirac particle in the presence of gravity requires that spacetime is not only curved, but also has a nonzero torsion. The coupling between the spin and torsion in the Einstein–Cartan theory of gravity generates gravitational repulsion at extremely high densities, which prevents a singularity in a black hole and may create there a new, closed, baby universe undergoing one or more nonsingular bounces. We show that quantum particle production caused by an extremely high curvature near a bounce creates enormous amounts of matter and can generate a finite period of inflation. Our scenario has only one parameter, does not depend significantly on the initial conditions, does not involve hypothetical scalar fields, avoids eternal inflation, and predicts plateau-like inflation that is supported by the Planck observations of the cosmic microwave background. This scenario suggests that our Universe may have originated from a nonsingular bounce in a black hole existing in another universe.