A Cosmological Uncertainty Relation and Late-Universe Acceleration

Original 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.