An alternative to usual dimensional reduction for gravity is analyzed, in the vielbein-spin connection formulation. Usual 4d Einstein gravity plus a topological term (the ”Born-Infeld” Lagrangian for gravity), is shown to be obtained by a generalized dimensional reduction from 5d Chern-Simons gravity. Chern-Simons gravity in d=2n+1 is dimensionally reduced to CS gravity in d=2n-1 via a mechanis...

Quantum Gravity is quite elusive at the experimental level; thus a lot of interest has been raised by recent searches for quantum gravity effects in the propagation of light from distant sources, like gamma ray bursters and active galactic nuclei, and also in earth-based interferometers, like those used for gravitational wave detection. Here we describe a simple heuristic picture of the quantum...

We review applications of noncommutative geometry in canonical quantum gravity. First, we show that the framework of loop quantum gravity includes natural noncommutative structures which have, hitherto, not been explored. Next, we present the construction of a spectral triple over an algebra of holonomy loops. The spectral triple, which encodes the kinematics of quantum gravity, gives rise to a...

Simplicial quantum gravity is an approach to quantizing gravity by using as a regularization scheme dynamical triangulations of riemannian manifolds. In dimension two, such an approach has led to considerable progress in our understanding of 2D-gravity. In dimension three and four, the current state of affairs is less favourable, and dynamically triangulated models of quantum gravity suffer fro...

We analyze the perturbative implications of the most general high derivative approach to quantum gravity based on a diffeomorphism invariant local action. In particular, we consider the super-renormalizable case with a large number of metric derivatives in the action. The structure of ultraviolet divergences is analyzed in some detail. We show that they are independent of the gauge fixing condi...

We analyze the perturbative implications of the most general high derivative approach to quantum gravity based on a di eomorphism invariant local action. In particular, we consider the super-renormalizable case with a large number of metric derivatives in the action. The structure of ultraviolet divergences is analyzed in some detail. We show that they are independent of the gauge xing conditio...

Using the Born-Oppenheimer idea we show that the Wheeler-DeWitt equation in an oscillating regime can also allow a different type of semiclassical quantum gravity that preserves completely the unitary quantum evolution of a matter field, which reduces the same asymptotic limit as the others. We develop a perturbation method to find the quantum corrections of a matter field to the gravity. The s...

The different approaches to quantum gravity, almost all of which are described in detail in the rest of this volume, can be classified according to what they say about spacetime and gravity. First, there are the quantum field theory-like approaches (string theory, black hole thermodynamics, etc.). It is natural to push quantum field theory to its limits since it is our best theory so far. Resul...

Affine quantum gravity, which differs notably from either string theory or loop quantum gravity, is briefly reviewed. Emphasis in this article is placed on the use of affine coherent states in this program.