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arXiv · 1412.6000

Rainbow metric from quantum gravity

Mehdi Assanioussi·Andrea Dapor·Jerzy Lewandowski
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Abstract

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 space-time. Under general assumptions, we discover that the quantum space-time on which the field propagates can be replaced by a classical space-time, 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 behavior of high-energy particles on quantum space-time relies only on the assumption that the quantum space-time is described by a wave-function $Ψ_o$ in a Hilbert space $\mathcal{H}_G$.

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Mehdi Assanioussi, Andrea Dapor, Jerzy Lewandowski. 2015-10-28. Rainbow metric from quantum gravity. https://doi.org/10.1016/j.physletb.2015.10.043

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