A Cosmological Uncertainty Relation and Late-Universe Acceleration

TL;DR

This paper introduces a quantum-inspired modification to cosmological equations, linking universe size and expansion rate uncertainty, predicting late-time acceleration or a bounce without new particles.

Contribution

It proposes a deformed commutation relation affecting the Friedmann equation, connecting quantum uncertainty to cosmic acceleration and singularity resolution.

Findings

Predicts late-time dark energy with w > -1 for positive exponent

Produces a non-singular bounce for negative exponent

Preserves primordial power spectrum without new particles

Abstract

We propose that the size of the universe and its rate of expansion cannot be simultaneously specified with arbitrary precision, a quantum mechanical statement encoded in a deformed commutation relation for the scale factor. The deformation modifies the Friedmann equation by adding a geometric correction to the expansion rate, and the sign and magnitude of a single free exponent determine the cosmological behavior. When the exponent is positive, the model predicts late-time dark energy with $w > -1$, testable with current and next-generation surveys. When the exponent is sufficiently negative, the same deformation produces a non-singular classical bounce that resolves the Big Bang singularity. The model introduces no new particles or fields and preserves a scale-invariant primordial power spectrum. The deformation has a natural interpretation as a horizon-scale phenomenon, with the cosmological horizon, and not the Planck length, setting its characteristic scale. The late-universe regime is then its generic application, with the expansion history as the primary observable signature. Cosmic acceleration may be the macroscopic imprint of quantum gravity at the cosmological horizon.