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arXiv · 1211.0161

Metric emerging to massive modes in quantum cosmological space-times

Andrea Dapor·Jerzy Lewandowski
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Abstract

We consider a massive quantum test Klein-Gordon field probing an isotropic quantum cosmological space-time in the background. The result obtained is surprising. It turns out, that despite the isotropy of the quantum gravitational field, the semi-classical metric experienced by a mode of the K-G field is non-isotropic. The anisotropy depends on the direction of the momentum of the mode. Specifically, what we do is to derive a semi-classical space-time which emerges to a mode of the field. The method amounts to a comparison between QFT on a quantum background and QFT on a classical curved space-time, giving rise to an emergent metric tensor. The components of the semi-classical metric tensor are calculated from the equation of propagation of the quantum K-G field in the test field approximation. The anisotropies are of a quantum nature: they are proportional to Planck constant and "dress" the isotropic classical space-time obtained in the classical limit.

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Andrea Dapor, Jerzy Lewandowski. 2013-05-10. Metric emerging to massive modes in quantum cosmological space-times. https://doi.org/10.1103/physrevd.87.063512

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