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arXiv · 1505.05021

Vacuum fluctuations in theories with deformed dispersion relations

Michele Arzano·Giulia Gubitosi·Joao Magueijo·Giovanni Amelino-Camelia
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Abstract

We examine vacuum fluctuations in theories with modified dispersion relations which represent dimensional reduction at high energies. By changing units of energy and momentum we can obtain a description rendering the dispersion relations undeformed and transferring all the non-trivial effects to the integration measure in momentum space. Using this description we propose a general quantization procedure, which should be applicable whether or not the theory explicitly introduces a preferred frame. Based on this scheme we evaluate the power spectrum of quantum vacuum fluctuations. We find that in {\it all} theories which run to 2 dimensions in the ultraviolet the vacuum fluctuations, in the ultraviolet regime, are scale-invariant. This is true in flat space but also for "inside the horizon" modes in an expanding universe. We spell out the conditions upon the gravity theory for this scale-invariance to be preserved as the modes are frozen-in outside the horizon. We also digress on the meaning of dimensionality (in momentum and position space) and suggest that the spectral index could itself provide an operational definition of dimensionality.

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Michele Arzano, Giulia Gubitosi, Joao Magueijo, Giovanni Amelino-Camelia. 2015-06-15. Vacuum fluctuations in theories with deformed dispersion relations. https://arxiv.org/abs/1505.05021

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