The recent discovery of two flux decrements in deep radio maps obtaine
d by the VLA and the Ryle Telescope can have powerful implications for
the density parameter of the Universe, Omega(o). We outline these imp
lications by modeling the decrements as the thermal Sunyaev-Zel'dovich
(SZ) effect from two clusters assuming their properties are similar t
o those of the low redshift population. In this case, the absence of a
ny optical or X-ray counterparts argues that the clusters must be at l
arge redshifts. We highlight the difficulty this poses for a critical
cosmology by a comparison with a fiducial open model with Omega(o) = 0
.2 (lambda(o) = 0). Applying the phenomenological X-ray luminosity-tem
perature relation needed to explain the EMSS cluster redshift distribu
tion, as inferred by Oukbir and Blanchard (1997), we convert the X-ray
band upper limits to lower limits on the clusters' redshifts. Compari
son of the counts implied by these two SZ detections with model predic
tions, for clusters with redshifts larger than these lower limits, ill
ustrates quantitatively the inability of the critical cosmology to acc
ount for such high-redshift clusters. On the other hand, the open mode
l with Omega(o) = 0.2 remains consistent with the existence of the two
objects; it possibly has, however, difficulties with current limits o
n spectral distortions and temperature fluctuations of the cosmic micr
owave background. The discussion demonstrates the value of SZ cluster
searches for testing cosmological models and theories of structure for
mation.