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Prominent approaches to quantum gravity struggle when it comes to incorporating a positive cosmological constant in their models. Using quantization of a complex $\mathrm{SL}(2,\mathbb{C})$ Chern-Simons theory we include a cosmological…
Some approaches to Quantum Gravity (QG) entail decoherence of quantum matter propagating in it, due to an ``environment'' of QG degrees of freedom inaccessible to low-energy observers. In the first part of this talk, I discuss potential,…
The geometro-stochastic method of quantization provides a framework for quantum general relativity, in which the principal frame bundles of local Lorentz frames that underlie the fibre-theoretical approach to classical general relativity…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
We study K\"{a}hler gravity on local SU(N) geometry and describe precise correspondence with certain supersymmetric gauge theories and random plane partitions. The local geometry is discretized, via the geometric quantization, to a foam of…
A calculational scheme of quantum-gravitational effects on the physical quantities is proposed. The calculations are performed in 4-$\epsilon$ dimension with $1/N$-expansion scheme, where the Einstein gravity is renormalizable and it has an…
We investigate the possibility that a background independent quantum theory of gravity is not a theory of quantum geometry. We provide a way for global spacetime symmetries to emerge from a background independent theory without geometry. In…
The building blocks of a quantum theory of general relativity are expected to be discrete structures. Loop quantum gravity is formulated using a basis of spin networks (wave functions over oriented graphs with coloured edges), thus…
Quantum gravity is understood as a theory that, in some sense, unifies general relativity (GR) and quantum theory, and is supposed to replace GR at extremely small distances (high-energies). It may be that quantum gravity represents the…
Emergent modified gravity is a post-Einsteinian gravitational theory where spacetime geometry is not fundamental but rather emerges from the gravitational degrees of freedom in a non-trivial way. The specific relationship between geometry…
Often, geometries with horizons offer insights into the intricate relationships between general relativity and quantum physics. However, some subtle aspects of gravitating quantum systems might be difficult to ascertain using static…
We review recent developments in differential topology with special concern for their possible significance to physical theories, especially general relativity. In particular we are concerned here with the discovery of the existence of…
Phenomenological approaches to quantum gravity implement a minimum resolvable length-scale but do not link it to an underlying formalism describing geometric superpositions. Here, we introduce an intuitive approach in which points in the…
We present a new, falsifiable, quantum theory of gravity, which we name Non-commutative Matter-Gravity. The commutative limit of the theory is classical general relativity. In the first two papers of this series, we have introduced the…
This series of lectures gives a simple and self-contained introduction to the non-perturbative and background independent loop approach of canonical quantum gravity. The Hilbert space of kinematical quantum states is constructed and a…
Each approach to the quantum-gravity problem originates from expertise in one or another area of theoretical physics. The particle-physics perspective encourages one to attempt to reproduce in quantum gravity as much as possible of the…
An earlier proposed theory with linear-gonihedhic action for quantum gravity is reviewed. One can consider this theory as a "square root" of classical gravity with a new fundamental constant of dimension one. We demonstrate also, that the…
In this paper, I emphasize those features of the extended phase space approach to quantization of gravity that distinguish it among other approaches. First of all, it is the conjecture about non-trivial topology of the Universe which was…
In recent years, a close connection between supergravity, string effective actions and generalized geometry has been discovered that typically involves a doubling of geometric structures. We investigate this relation from the point of view…
This paper explores the theoretical implications of quantum gravity by analyzing compact stellar objects, presenting three distinct models that serve as alternatives to traditional black holes. These models are characterized by their…