A limit on Planck-scale froth with ESPRESSO

Pettini, Max; Fumagalli, Michele; Welsh, Louise; Cooke, Ryan

Abstract

Some models of quantum gravity predict that the very structure of space–time is ‘frothy’ due to quantum fluctuations. Although the effect is expected to be tiny, if these space–time fluctuations grow over a large distance, the initial state of a photon, such as its energy, is gradually washed out as the photon propagates. Thus, in these models, even the most monochromatic light source would gradually disperse in energy due to space–time fluctuations over large distances. In this paper, we use science verification observations obtained with ESPRESSO at the Very Large Telescope to place a novel bound on the growth of space–time fluctuations. To achieve this, we directly measure the width of a narrow Fe II absorption line produced by a quiescent gas cloud at redshift z ≃ 2.34, corresponding to a comoving distance of ≃5.8 Gpc. Using a heuristic model where the energy fluctuations grow as σE/E = (E/EP)α, where EP ≃ 1.22 × 1028 eV is the Planck energy, we rule out models with α ≤ 0.634, including models where the quantum fluctuations grow as a random walk process (α = 0.5). Finally, we present a new formalism where the uncertainty accrued at discrete space–time steps is drawn from a continuous distribution. We conclude, if photons take discrete steps through space–time and accumulate Planck-scale uncertainties at each step, then our ESPRESSO observations require that the step size must be at least ≳ 1013.2lP, where lP is the Planck length.

Citation

Pettini, M., Fumagalli, M., Welsh, L., & Cooke, R. (2020). A limit on Planck-scale froth with ESPRESSO. Monthly Notices of the Royal Astronomical Society, 494(4), 4884-4890. https://doi.org/10.1093/mnras/staa440

• Journal Article Type: Article
• Acceptance Date: Feb 11, 2020
• Online Publication Date: May 6, 2020
• Publication Date: 2020-06
• Deposit Date: Jun 24, 2020
• Publicly Available Date: Jun 24, 2020
• Journal: Monthly Notices of the Royal Astronomical Society
• Print ISSN: 0035-8711
• Electronic ISSN: 1365-2966
• Publisher: Royal Astronomical Society
• Peer Reviewed: Peer Reviewed
• Volume: 494
• Issue: 4
• Pages: 4884-4890
• DOI: https://doi.org/10.1093/mnras/staa440
• Public URL: https://durham-repository.worktribe.com/output/1262009