FAU^2 Mini-Workshop on Loop Quantum Gravity

2 May 2023, 14:00 → 3 May 2023, 18:30 Europe/Berlin

ECAP Laboratory Building

The mini workshop is organized to promote scientific exchange between the quantum gravity groups at Florida Atlantic University (FAU) and FAU Erlangen-Nürnberg. The workshop topics include current research topics in quantum gravity in both the canonical and covariant formalisms. Next to some external speakers in particular, this workshop offers also junior scientists in the groups at the two FAU's to present their current research projects. 

Organizers: Kristina Giesel and Muxin Han

Tuesday 2 May

Session 1

1 Symmetry charges in reduced phase space and their algebra

The investigation of boundary charges in asymptotically flat spacetime drew a lot of attention in recent years, which has provided us valuable insight and significantly enhanced our general understanding of gravity. However, most of previous studies along this line are based on the traditional general relativity, which is a pure constraint theory in the bulk. The boundary charges based on the reduced phase are less known to the community. In this talk, I will discuss our recent progress in the symmetry charges (including the bulk parts and the boundary parts) in the reduced phase space based on the Brown-Kuchaˇr Formalism. In this work, we introduce specific asymptotically flat boundary conditions to make the variation of the physical Hamiltonian well-defined. Using these boundary conditions, we construct the boundary-preserving symmetries, including supertranslations and superrotations. The algebra of these symmetry generators is given by the Poisson brackets, which contains a center extension.

Speaker: Hongwei Tan

2 Edge modes and quantum reference frames in linearized gravity

A common way to interpret the coordinate invariance of Einstein’s equations is to say that coordinates are a mere gauge redundancy and play no physical role themselves. This is no longer true when we restrict ourselves to subsystems localized in a compact but otherwise arbitrary domain. At the boundary of the domain, coordinate transformations are no longer gauge redundant. The then necessary boundary conditions brake the gauge symmetries of the theory in the bulk. Otherwise unphysical gauge redundancies take on physical meaning as physical boundary modes (edge modes). In my talk, I present two recent developments on this frontier. First of all, I will speak about how to connect the research on edge modes to the geometry of open systems, dissipation and entropy production via the framework of metriplectic geometry. The second part of the talk deals with perturbative gravity. Taking a decoupling limit, where the Newton constant is sent to zero, we characterize the local phase space of the gravitational field in a finite region. Phase space splits into radiation modes and additional edge modes that are dual to reference frames at the boundary. Taking the boundary to infinity, we obtain a new quantum representation of asymptotic symmetries in perturbative gravity. The resulting infinite-dimensional group of boundary symmetries is the group of asymptotic Bondi–Metzner–Sachs (BMS) transformations at spacelike infinity. In this way, our results extend the existing notions of quantum reference frames and make them applicable to the framework of asymptotic symmetries and weak fields.
The talk is based on [arXiv:2206.00029] and [arXiv:2302.11629].

Speaker: Wolfgang Wieland

Coffee break

Session 2

3 A master equation for gravitationally induced decoherence of a scalar field using Ashtekar variables

In the talk, we present the derivation of a decoherence model
containing a scalar field coupled to a gravitational environment. With such models the influence of the quantum gravitational environment on the scalar field’s dynamics can be analysed. Starting with full general relativity in Ashtekar's connection formulation, we focus on weak gravitational interactions in an asymptotically flat universe and the scalar field as matter component. We apply a reduced phase space quantisation of the model by means of choosing suitable Dirac observables and apply a Fock quantisation to the reduced phase space. The quantised system is then treated as an open quantum system with gravity as the environment. With the help of the projection operator technique, we derive a second order time-convolutionless master equation. This equation is an effective evolution equation which encodes the temporal evolution of the scalar field in terms of certain operators, whose form is a result of the model under consideration and several physical assumptions. These operators arise when taking the trace over the gravitational environment and lead to physical effects like dissipation or
decoherence of the matter field induced by gravity. Finally, we briefly discuss possible applications of the model's master equation.

Speaker: Max Joseph Fahn

Final Discussion with all speakers: Final discussion

Workshop Dinner

Wednesday 3 May

Session 3

4 Early Dark Energy: a status update and new constraints using the profile likelihood

Early dark energy (EDE) is a dark energy-like component in the early universe, which was proposed to solve the Hubble tension, a discrepancy between different measurements of the current expansion rate of the universe. Currently, there is no consensus in the literature as to whether EDE can simultaneously solve the Hubble tension and provide an adequate fit to the data from the cosmic microwave background and the large-scale structure of the universe. In this talk, I will give a brief overview on the status of EDE and describe the disagreement about EDE in the literature. To explore the origin of this disagreement, we use a profile likelihood analysis and find evidence that the constraints on EDE from Markov Chain Monte Carlo analyses are influenced by prior volume effects. Using the profile likelihood we construct constraints on the Hubble constant and the fraction of EDE, which are free from these effects, and find that EDE presents a viable solution to the Hubble tension while presenting a good fit to cosmological data sets.

Speaker: Laura Herold

5 Radiative correction of 4D spinfoam model with a cosmological constant

Infrared divergence is a common feature of spinfoam models with a vanishing cosmological constant. The disappearance of divergence at the present of a non-zero cosmological constant was conjectured and then recently proved in a spinfoam model constructed with complex Chern-Simons theory. It has been an active research area to study how such divergence depends on the value of the cosmological constant.

In this talk, I will present our recent results on the first-order divergence, also called the radiative correction, of a 4D spinfoam model with a cosmological constant. It is based on the recently constructed spinfoam model with complex SL(2, C) Chern-Simons theory. Taking the cosmological constant to approach the zero limit, our analysis gives a lower bound on the divergence, which is an inverse power law in (the absolute value of) the cosmological constant.

Speaker: Qiaoyin Pan

Coffee break

Session 4

6 Complex critical point and effective dynamics of spinfoam quantum gravity

This talk will be based on the paper arXiv:2301.02930. I will introduce the complex critical points in the 4-dimensional Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model in the large-$j$ regime. For the 4-simplex amplitude, taking into account the complex critical point generalizes the large-$j$ asymptotics to the situation with non-Regge boundary data and relates to the twisted geometry. For generic simplicial complexes, I will present a general procedure to derive the effective theory of Regge geometries from the spinfoam amplitude in the large-$j$ regime by using the complex critical points. The effective theory is analyzed in detail for the spinfoam amplitude on the double-$\Delta_3$ simplicial complex.

Speaker: Dongxue Qu

7 On consistent gauge-fixing conditions in polymerized gravitational systems

Gauge fixing is a standard method for deriving the physical sector of a gauge theory. In the context of symmetry reduced models of loop quantum gravity a polymerisation has been applied to gauge fixed models to obtain so called effective theories that mimic the underlying quantum theory to some extend. Motivated from the question whether gauge fixing and polymerization commute, in this talk we will discuss the subtleties of implementing dynamical consistent gauge fixings in the effective theory and present a procedure to determine in a given model the effective lapse and shift. Although we can proof for a range of models that gauge fixing and polymerization does indeed commute and discuss consequences, for most models in the literature this is not the case. We further discuss how for a given choice of effective lapse and/or shift one can obtain a corresponding gauge fixing condition and show that in general this requires non-standard polymerisations or gauge fixing conditions with different classical limits.

Speaker: Stefan Weigl

Final discussion with all speakers: Final discussion