Cut-sky orthogonal mode analyses of the COBE-DMR 53 and 90 GHz sky map
s are used to determine the normalization of a variety of open cosmogo
nical models based on the cold dark matter scenario. To constrain the
allowed cosmological parameter range for these open cosmogonies, the p
redictions of the DMR-normalized models are compared to various observ
ational measures of cosmography and large-scale structure, viz., the a
ge of the universe; small-scale dynamical estimates of the clustered-m
ass density parameter Omega(0); constraints on the Hubble parameter h,
the X-ray cluster baryonic-mass fraction Omega(B)/Omega(0), and the m
atter power spectrum shape parameter; estimates of the mass perturbati
on amplitude; and constraints on the large-scale peculiar velocity hel
d. The open-bubble inflation model (Ratra & Peebles; Bucher, Goldhaber
, & Turok; Yamamoto, Sasaki, & Tanaka) is consistent with current dete
rminations of the 95% confidence level (c.l.) range of these observati
onal constraints, provided 0.3 < Omega(0) less than or similar to 0.6
(similar to 95% c.l.). More specifically, for a range of h, the model
is reasonably consistent with recent high-redshift estimates of the de
uterium abundance that suggest Omega(B)h(2) similar to 0.007, provided
Omega(0) similar to 0.35; recent high-redshift estimates of the deute
rium abundance that suggest Omega(B)h(2) similar to 0.02 favor Omega(0
) similar to 0.5, while the old nucleosynthesis value Omega(B)h(2) = 0
.0125 requires Omega(0) similar to 0.4. Small shifts in the inferred C
OBE-DMR normalization amplitudes due to (1) the small differences betw
een the galactic-and ecliptic-coordinate sky maps, (2) the inclusion o
r exclusion of the quadrupole moment in the analysis, (3) the faint hi
gh-latitude Galactic emission treatment, and (4) the dependence of the
theoretical cosmic microwave background anisotropy angular spectral s
hape on the value of h and Omega(B), are explicitly quantified. Corres
ponding variations in the likelihood fits of models to the DMR data th
en imply that the DMR data alone do not possess sufficient discriminat
ive power to prefer any values for Omega(0), h, or Omega(B), at the 95
% c.l. for the models considered. At a lower c.l., and when the quadru
pole moment is included in the analysis, the DMR data are most consist
ent with either Omega(0) less than or similar to 0.1 or Omega(0) simil
ar to 0.7 (depending on the model considered). However, when the quadr
upole moment is excluded from the analysis, the DMR data are most cons
istent with Omega(0) similar to 0.35-0.5 in all open models considered
(with 0.1 less than or equal to Omega(0) less than or equal to, 1), i
ncluding the open-bubble inflation model. Earlier claims (Yamamoto & B
unn; Bunn & White) that the DMR data require a 95% c.l. lower bound on
Omega(0) (similar to 0.3) are not supported by our (complete) analysi
s of the 4 year data: the DMR data alone cannot be used to constrain O
mega(0) meaningfully.