This series consists of talks in the area of Quantum Gravity.
We will review the gravitational formula for fine grained entropy. We will discuss how it applies to an evaporating black hole and how we can compute the entropy of Hawking radiation.
In this talk I will discuss some recent results on boundary degrees of freedom (or edge modes), and their description via an extended phase space structure containing extra boundary fields. Motivated by a slight modification of the covariant phase space formalism, I will show how the use of a boundary Lagrangian enables to include the edge modes in the phase space and to obtain their boundary dynamics. This will be illustrated on the example of Maxwell theory, where in addition the edge modes can be understood as contributing to entanglement entropy.
Our earlier findings indicate the violation of the 'volume simplicity' constraint in the current Spinfoam models (EPRL-FK-KKL). This result, and related problems in LQG, promted to revisit the metric/vielbein degrees of freedom in the classical Einstein-Cartan gravity. Notably, I address in detail what constitutes a 'geometry' and its 'group of motions' in such Poincare gauge theory. In a differential geometric scheme that I put forward the local translations are not broken but exact, and their relation to diffeomorphism transformations is clarified.
In this talk, I will describe the framework of large D matrix models, which provides new limits for matrix models where the sum over planar graphs simplifies when D is large. The basic degrees of freedom are a set of D real matrices of size NxN which is invariant under O(D). These matrices can be naturally interpreted as a real tensor of rank three, making a compelling connection with tensor models. Furthermore, they have a natural interpretation in terms of D-brane constructions in string theory.
According to the Asymptotic Safety conjecture, a (non-perturbatively)
renormalizable quantum field theory of gravity could be constructed
based on the existence of a non-trivial fixed point of the
renormalization group flow.
The existence of this fixed point can be established, e.g., via the
non-perturbative methods of the functional renormalization group (FRG).
In practice, the use of the FRG methods requires to work within
truncations of the gravitational action, and higher-derivative operators
Hopf algebra lattice models are related to certain topological quantum field theories and give rise to topological invariants of oriented surfaces. Examples are the combinatorial quantisation of Chern-Simons theory and the Kitaev model.
In approaches to quantum gravity, where smooth spacetime is an emergent approximation of a discrete Planckian fundamental structure, any standard effective field theoretical description will miss part of the degrees of freedom and thus break unitarity. Here we show that these expectations can be made precise in loop quantum cosmology.
Cosmological perturbation theory has a long tradition for describing the early phases of the Universe. As the observations of the CMB radiation suggest, it is reasonable, at least as a first approximation, to implement cosmological inhomogeneities as small perturbations around homogeneous and isotropic FRW solutions. In these approaches, backreactions between the inhomogeneities and the background are usually neglected. There is an ongoing debate about how and to which extend these backreactions affect the large scale structure of the Universe.
I will explain how dark energy in cosmology could arise from the
noisy diffusion of energy from the low energy degrees of freedom of matter (described in terms of QFT)
to the fundamental Planckian granularity (expected from quantum gravity). This
perspective leads to a natural model resolving the fine tuning problem associated to the small
value of the cosmological constant. However, recent observations suggest that the dark energy
component in our universe might not be constant and should instead have grown from the recombination time to the present.