Quantum Gravity

Our understanding of the physical world at the most fundamental level is based on two theories: quantum theory and general relativity. They are impressively successful when each is considered on its own, but in situations where both play a role, we are reduced to puzzles and absurdity. To the great frustration of researchers, candidate theories of quantum gravity produce more puzzles than answers. We shall tour of some of the problems, focusing on the role of spacetime and causality. We will consider the possibility that spacetime did not always exist but is instead emergent and explore how one can create a spacetime from a world with no notion of "here" and "there".

The idea behind an intersection between loop quantum gravity and noncommutative geometry is to combine elements of unification with a setup of canonical quantum gravity. In my talk I will first review the construction of a semi-finite spectral triple build over an algebra of holonomy loops. Here, the loop algebra is a noncommutative algebra of functions over a configurations space of connections, and the interaction between the Dirac type operator and the loop algebra captures information of the kinematical part of canonical quantum gravity. Next, I will show how certain normalizable, semi-classical states are build which connects the spectral triple construction to the Dirac Hamiltonian in 3+1 dimensions. Thus, these states can be interpreted as one-particle fermion states in an ambient gravitational field. This analysis indicates that the spectral triple construction involves matter degrees of freedom.

Cosmology and cosmological implications of quantum gravity. Observable effects in cosmology help to identify the limits of general relativity, which could potentially be surpassed by modified theories of gravity and/or quantum gravity.

Mathematical aspects of modern theories of elementary particles and gravitation. Replacing the notion of particles with fundamental abstract fields (magnetic monopoles, vortices and Skyrmions) in an attempt to approach a formulation for quantum gravity.

Collisions and subsequent decays of higher dimensional branes leave behind three-dimensional branes, one of which could play the role of our universe. This process also leads to the production of one-dimensional branes, D-strings, and fundamental ones (F-strings), known as cosmic superstrings. In the first part of this talk, I will discuss the mechanism we have proposed in order to explain the origin of the space-time dimensionality, while in the second part I will review formation and dynamics of cosmic superstrings.