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

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 ?0 in the context of inflation-based cold dark matter (CDM) models with no cosmological constant. We use ?2 minimization to explore the four-dimensional parameter space having as free parameters, h, ?0, the power-spectrum slope n, and the power-spectrum normalization at ? = 10. Conditioning on ?0 = 1, we obtain h = 0.33 ? 0.08. Allowing ?0 to be a free parameter reduces the ability of the CMB data to constrain h, and we obtain 0.26 0.53. A strong correlation between acceptable h and ?0 values leads to a new constraint ?0h1/2 = 0.55 ? 0.10. We quote ??2 = 1 contours as error bars; however, because of nonlinearities of the models, these may be only crude approximations to 1 ? confidence limits. A favored open model with ?0 = 0.3 and h = 0.70 is more than ~4 ? from the CMB data best-fit model and is rejected by goodness-of-fit statistics at the 99% confidence level. High baryonic models (?bh2 ~ 0.026) yield the best CMB ?2 fits and are more consistent with other cosmological constraints. The best-fit model has n = 0.91 -->+ 0.29?0.09 and Q10 = 18.0 -->+ 1.2?1.5 ?K. Conditioning on n = 1, we obtain h = 0.55 -->+ 0.13?0.19, ?0 = 0.70 with a lower limit ?0 > 0.58, and Q10 = 18.0 -->+ 1.4?1.5 ?K. The amplitude and position of the dominant peak in the best-fit power spectrum are Apeak = 76 -->+ 3?7 ?K and ?peak = 260 -->+ 30?20. Unlike the ?0 = 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 ?0 0.85. Using an approximate joint likelihood to combine our CMB constraint on ?0h1/2 with other cosmological constraints, we obtain h = 0.58 ? 0.11 and ?0 = 0.65 -->+ 0.16?0.15.