Quantum uncertainty in the horizon size in an inflationary universe

Abstract

It is shown that uncertainty principle prevents simultaneous, exact measurement of the expansion factor S(t) and its time derivative Ṡ(t) in a FRW universe. We compute the uncertainties in these parameters in the semiclassical limit. It is shown that (i) there is a minimum uncertainty ΔlH in the Hubble distance lH(t)=(Ṡ/S)−1 in a semiclassical universe. (ii) this uncertainty is amplified to an unacceptably large value if there was an inflationary phase in the early universe.