Cosmological uncertainty relation and late-universe acceleration
Phys. Rev. D 114, 043525 – Published 13 August, 2026
DOI: https://doi.org/10.1103/zgnd-h2xv
Abstract
We propose that the size of the universe and its expansion rate cannot be simultaneously specified with arbitrary precision—a quantum mechanical uncertainty encoded via a deformed commutation relation for the scale factor. This deformation introduces a geometric correction to the Friedmann equation, where the resulting cosmological dynamics are governed entirely by the sign and magnitude of a single free exponent. For a positive exponent, the model predicts late-time dark energy with , leaving a distinct expansion history that is testable by current and next-generation large-scale structure surveys. Conversely, a sufficiently negative exponent yields a nonsingular classical bounce, resolving the big bang singularity. Notably, the model requires no exotic particles or fields and preserves a scale-invariant primordial power spectrum. Rather than operating at the Planck length, this deformation naturally manifests as a horizon-scale phenomenon set by the cosmological horizon. Within this framework, cosmic acceleration emerges as the macroscopic imprint of quantum gravity at the cosmological horizon.
