Seminar of Theory of Relativity and Gravitation

I will describe a general mechanism for emergence of a rainbow metric from quantum gravity. This idea is based on QFT on a quantum spacetime. I will show that, under general assumptions, the fundamental quantum spacetime on which the field propagates can be described by a classical metric. It turns out that this effective metric depends explicitly on the mode of the field: as shown by an analysis of dispersion relations, quanta of different energy propagate on different metrics, similar to photons of different colors in a refractive material (hence the name ''rainbow''). In deriving this result I do not consider any specific theory of quantum gravity: the qualitative behavior of high-energy particles on quantum spacetime relies only on the assumption that the quantum spacetime is described by a wave-function in a Hilbert space.