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Rainbow metric from quantum gravity
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DOI：10.1016/j.physletb.2015.10.043.png)
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Abstract
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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 psi(o) in a Hilbert space H-G. (C) 2015 The Authors. Published by Elsevier B.V.
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