Rainbow metric from quantum gravity

• Main Authors: Mehdi Assanioussi, Andrea Dapor, Jerzy Lewandowski
• Format: Article
• Language: English
• Published: Elsevier 2015-12-01
• Series: Physics Letters B
• Online Access: http://www.sciencedirect.com/science/article/pii/S0370269315008023

In this Letter, we describe a general mechanism for emergence of a rainbow metric from a quantum cosmological model. This idea is based on QFT on a quantum spacetime. Under general assumptions, we discover that the quantum spacetime on which the field propagates can be replaced by a classical spacetime, whose metric depends explicitly on the energy of the field: as shown by an analysis of dispersion relations, quanta of different energy propagate on different metrics, similar to photons in a refractive material (hence the name “rainbow” used in the literature). In deriving this result, we do not consider any specific theory of quantum gravity: the qualitative behaviour of high-energy particles on quantum spacetime relies only on the assumption that the quantum spacetime is described by a wave-function Ψo in a Hilbert space HG.