  We discuss a formalism where a universe is identified with the support of a
wave function propagating through space-time. As opposed to classical
cosmology, the resulting universe is not a spacelike section of some
space-time, but a hyper-layer of a finite timelike width, a set which is not a
three-dimensional submanifold of space-time. We test the formalism on the
example of a universe that contains a single harmonic oscillator (a
generalization of the curvature-dependent Cari\~nena-Ra\~nada-Santander (CRS)
model). As opposed to the original CRS formulation, here the curvature is not a
parameter but a quantum observable, a function of the world-position operator.
It is shown that asymptotically, for large values of the invariant evolution
parameter $\tau$, one reconstructs the standard quantum results, with one
modifiication: The effective (renormalized) mass of the oscillator decreases
with $\tau$. The effect does not seem to be a peculiarity of harmonic
oscillators, so one may speculate that masses of distant elementary quantum
systems are greater from their values known from our quantum mechanical
measurements.
