Angular spectrum of quantum fluctuations in causal structure

Craig Hogan; Ohkyung Kwon; Nathaniel Selub

doi:10.1103/PhysRevD.109.123505

paper

Angular spectrum of quantum fluctuations in causal structure

arXiv:2303.06563 · doi:10.1103/PhysRevD.109.123505

Abstract

Scaling arguments are used to constrain the angular spectrum of distortions on boundaries of macroscopic causal diamonds, produced by Planck-scale vacuum fluctuations of causally-coherent quantum gravity. The small-angle spectrum of displacement is derived from a form of scale invariance: the variance and fluctuation rate of distortions normal to the surface of a causal diamond of radius $R$ at transverse physical separation $c τ ≪ R$ should depend only on $τ$ , with a normalization set by the Planck time $t_{P}$ , and should not depend on $R$ . For measurements on scale $R$ , the principle leads to universal scaling for variance on angular scale $Θ$ , $⟨ δ τ^{2} ⟩_{Θ} ≃ τ t_{p} \sim Θ R t_{P} / c$ , and angular power spectrum $C_{ℓ} \sim (R l_{P}) / ℓ^{3}$ at $ℓ ≫ 1$ . This spectrum is consistent with a relational model of holographic noise based on causally coherent virtual null gravitational shocks, a general picture conjectured for all $ℓ$ . The high $ℓ$ scaling is contrasted with that predicted in some other quantum models, which differ by one power of angular wavenumber $ℓ$ and are shown to predict excessive blurring of images from distant sources.

5 pages, 2 figures. PRD accepted version

Angular spectrum of quantum fluctuations in causal structure

Abstract

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