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

We use a combination of the most recent cosmic microwave background (CMB) flat-band power measurements to place constraints on Hubble’s constant h and the total density of the Universe Ωo in the context of inflation-based cold dark matter (CDM) models with no cosmological constant. We use χ2 minimization to explore the 4-dimensional parameter space having as free parameters, h, Ωo, the power spectrum slope n and the power spectrum normalization at ℓ = 10. Conditioning on Ωo = 1 we obtain h = 0.33 ± 0.08. Allowing Ωo to be a free parameter reduces the ability of the CMB data to constrain h and we obtain 0.26 < h < 0.97 with a best-fit value at h = 0.40. We obtain Ωo = 0.85 and set a lower limit Ωo> 0.53. A strong correlation between acceptable h and Ωo values leads to a new constraint Ωoh1/2 = 0.55 ±0.10. We quote ∆χ2 = 1 contours as error bars, however because of nonlinearities of the models, these may be only crude approximations to 1σ confidence limits. A favored open model with Ωo = 0.3 and h = 0.70 is more than ∼ 4σ from the CMB data best-fit model and is rejected by goodness-of-fit statistics at the 99 % CL. High