  COBE-normalized flat (matter plus cosmological constant) and open Cold Dark
Matter (CDM) models are tested by comparing their expected Hubble flow
variations and the observed variations in a Type Ia supernova sample and a
Tully Fisher cluster sample. The test provides a probe of the CDM power
spectrum on scales of $0.02h$ Mpc$^{-1}\la k\la 0.2h$ Mpc$^{-1}$, free of the
bias factor $b$. The results favor a low matter content universe, or a flat
matter-dominated universe with a very low Hubble constant and/or a very small
spectral index $n_{ps}$, with the best fits having $\Omega_0\sim 0.3$ to 0.4.
The test is found to be more discriminative to the open CDM models than to the
flat CDM models. For example, the test results are found to be compatible with
those from the X-ray cluster abundance measurements at smaller length scales,
and consistent with the galaxy and cluster correlation analysis of Peacock and
Dodds (1994) at similar length scales, if our universe is flat; but the results
are marginally incompatible with the X-ray cluster abundance measurements if
our universe is open. The open CDM results are consistent with that of Peacock
and Dodds only if the matter density of the universe is less than about 60% of
the critical density. The shortcoming of the test is discussed, so are ways to
minimize it.
