(keynote speaker)

Primordial fluctuations from loop quantum gravity

In modern cosmology there is an agreement that the seeds of structure formations reside in the quantum fluctuation of the geometry in the early universe, but there is no agreement about how these could be derived from a quantum theory of gravity. In this talk I present a proposal based on the covariant formulation of Loop Quantum Gravity. I describe how to define a wave function of the universe in this context, and how we can study fluctuations and correlations between spatial regions. The results obtained so far have been made possible by recent progress in numerical computations. I discuss the current state of this research program and the possible implications for modeling the early universe.