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We use a combination of the most recent cosmic microwave background (CMB)flat -band power measurements to place constraints on Hubble's constant h andthe total density of the Universe Omega_o in the context of inflation-basedcold dark matter (CDM) models with no cosmological constant. We use chisquaredminimization to explore the 4-dimensional parameter space having as freeparameters, h, Omega_o, the power spectrum slope n and the power spectrumnormalization at L=10. Conditioning on Omega_o=1 we obtain h=0.33 +/- 0.08.Allowing Omega_o to be a free parameter reduces the ability of the CMB data toconstrain h and we obtain 0.26 < h < 0.97 with a best-fit value at h=0.40. Weobtain Omega_o=0.85 and set a lower limit Omega_o > 0.53. A strong correlationbetween acceptable h and Omega_o values leads to a new constraint: Omega_oh^1/2=0.55 +/- 0.10. A favored open model with Omega_o=0.3 and h=0.70 is morethan ~4 sigma from the CMB data best-fit model and is rejected at the 99% CL.High baryonic models (Omega_b h^2 ~0.026) yield the best CMB chi-squared fitsand are more consistent with other cosmological constraints. The best-fit modelhas n=0.91^{+0.29}_{-0.09} and Q=18.0^+1.2_-1.5 uK. The amplitude and positionof the dominant peak in the best-fit power spectrum are A_peak=76^+3_-7 uK andL_peak = 260^+30_-20. Unlike the Omega_o=1 case we considered previously, CMB hresults are now consistent with the higher values favored by local measurementsof h but only if 0.55 >~ Omega_o >~ 0.85. Using an approximate joint likelihoodto combine our CMB constraint on Omegta_o h^{1/2} with other cosmologicalconstraints we obtain h=0.58 +/- 0.11 and Omega_o=0.65^+0.16_-0.15.Comment: 18 pages with 7 figures, conforms to accepted version in press:  Astrophysical Journal, 496, (April 1, 1998). Three of the figures have been  modified, references updated, typos corrected. This version includes a table  of current CMB measurement

What Can Cosmic Microwave Background Observations Already Say about Cosmological Parameters in Open and Critical‐Density Cold Dark Matter Models?