Uncertainty principle and the horizon size of our universe

Abstract

Quantum uncertainties prevent simultaneous measurement of the expansion factor S(t) and its time derivative$\dot S\left( t \right)$. Consequently the “Hubble size”$\left( {{{\dot S} \mathord{\left/ {\vphantom {{\dot S} S}} \right. \kern-\nulldelimiterspace} S}} \right)^{ - 1}$ has an inherent uncertainty in the quantum state that describes the semiclassical evolution of the universe. We show that the quantum uncertainty in the Hubble size of the universe is amplified to unacceptably large values in any inflationary process.