  We construct an extension of standard flat FLRW cosmology with matter,
possessing local D = 1, N = 1 proper-time supersymmetry. The fundamental
equation for the resulting mini-superspace models of quantum universes is a
Dirac-like analogue of the Friedmann and Wheeler-DeWitt equations. We provide
solutions of this equation for specific matter configurations based on the
supersymmetric O(3) and O(2, 1) sigma-models. It turns out that in the compact
model the volume rate of growth of the universe is quantized and non-vanishing
due to the zero-point energy of the scalar fields. In the non-compact model the
spectrum of the growth rates is continuous but subject to an uncertainty
relation involving the scale and the growth factor.
