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

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Abstract
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 Omega_o in the context of inflation-based cold dark matter (CDM) models with no cosmological constant. We use chisquared minimization to explore the 4-dimensional parameter space having as free parameters, h, Omega_o, the power spectrum slope n and the power spectrum normalization 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 to constrain h and we obtain 0.26 < h < 0.97 with a best-fit value at h=0.40. We obtain Omega_o=0.85 and set a lower limit Omega_o > 0.53. A strong correlation between acceptable h and Omega_o values leads to a new constraint: Omega_o h^1/2=0.55 +/- 0.10. A favored open model with Omega_o=0.3 and h=0.70 is more than ~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 fits and are more consistent with other cosmological constraints. The best-fit model has n=0.91^{+0.29}_{-0.09} and Q=18.0^+1.2_-1.5 uK. The amplitude and position of the dominant peak in the best-fit power spectrum are A_peak=76^+3_-7 uK and L_peak = 260^+30_-20. Unlike the Omega_o=1 case we considered previously, CMB h results are now consistent with the higher values favored by local measurements of h but only if 0.55 >~ Omega_o >~ 0.85. Using an approximate joint likelihood to combine our CMB constraint on Omegta_o h^{1/2} with other cosmological constraints we obtain h=0.58 +/- 0.11 and Omega_o=0.65^+0.16_-0.15.

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