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A state sum model based on the group SU(1,1) is defined. Investigations of its geometry and asymptotics suggest it is a good candidate for modelling (2+1) Lorentzian quantum gravity.
An alternative quantization of the gravitational Hamiltonian constraint of the $k=-1$ Friedmann-Robertson-Walker model is proposed by treating the Euclidean term and the Lorentzian term independently, mimicking the treatment of full loop…
We propose a generalization of Chiral Gravity, which follows from considering a Chern-Simons action for the spin connection with anti-symmetric contorsion. The theory corresponds to Topologically Massive Gravity at the chiral point…
We consider Lorentzian manifolds as examples of partially ordered measure spaces, sets endowed with compatible partial order relations and measures, in this case given by the causal structure and the volume element defined by each…
These are notes of introductory lectures on (a) elements of 2+1 dimensional gravity, (b) some aspects of its relation to Chern-Simons theory, (c) its generalization to couple higher spins, and (d) cosmic singularity resolution as an…
One of the main technical obstacles in constructing a consistent theory of quantum gravity is that the metric itself defines the causal structure required for quantization. This motivates implementing quantum aspects of gravity through an…
The equations of motion describing all physical systems, except gravity, remain invariant if a constant is added to the Lagrangian. In the conventional approach, gravitational theories break this symmetry exhibited by all other physical…
We define a three-dimensional quantum theory of gravity as the holographic dual of the Liouville conformal field theory. The theory is consistent and unitary by definition. The corresponding theory of gravity with negative cosmological…
In the Chern-Simons formulation of Einstein gravity in 2+1 dimensions the phase space of gravity is the moduli space of flat G-connections, where G is a typically non-compact Lie group which depends on the signature of space-time and the…
We consider the application of the consistent lattice quantum gravity approach we introduced recently to the situation of a Friedmann cosmology and also to Bianchi cosmological models. This allows us to work out in detail the computations…
We study the role of the Barbero-Immirzi parameter $\gamma$ and the choice of connection in the construction of (a symmetry-reduced version of) loop quantum gravity. We start with the four-dimensional Lorentzian Holst action that we reduce…
Recently Gambini and Pullin proposed a new consistent discrete approach to quantum gravity and applied it to cosmological models. One remarkable result of this approach is that the cosmological singularity can be avoided in a general…
The locally supersymmetric extension of the most general gravity theory in three dimensions leading to first order field equations for the vielbein and the spin connection is constructed. Apart from the Einstein-Hilbert term with…
Following the reasoning of Claudson and Halpern, it is shown that "fifth-time" stabilized quantum gravity is equivalent to Langevin evolution (i.e. stochastic quantization) between fixed non-singular, but otherwise arbitrary, initial and…
Making the Lorentzian path integral for quantum gravity well-defined and computable has been a long standing challenge. In this work we adopt the recently proposed effective spin foam models to the Lorentzian case. This defines a path…
We review and systematize recent attempts to canonically quantize general relativity in 2+1 dimensions, defined on space-times $\R\times\Sigma^g$, where $\Sigma^g$ is a compact Riemann surface of genus $g$. The emphasis is on quantizations…
Using as inspiration the well known chiral effective lagrangian describing the interactions of pions at low energies, in these lectures we review the quantization procedure of Einstein gravity in the spirit of effective field theories. As…
This proceeding is an introduction to cosmological applications of the Lorentz gauge theory. It provides the ingredients for a unique, though yet tentative $\Lambda$CDM theory of cosmology. The emergence of spacetime is described by the…
This paper contains applications of the quantum theory for gravity developed in the paper " A Sketch for a Quantum Theory of Gravity". Firstly, it is shown that the theory gives a direct derivation of the implications of Dirac's large…
We study the cosmological constant problem in a three-dimensional N=2 supergravity theory with gauge group SU[2]_{global}xU[1]_{local}. The model we consider is known to admit string-like configurations, the so-called semi-local cosmic…