Cosmological Parameters in Open and Critical - Density Cold Dark Matter Models ? 1

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 χ 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 Ωoh 1/2 = 0.55±0.10. We quote ∆χ = 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 baryonic models (Ωbh 2 ∼ 0.026) yield the best CMB χ fits and are more consistent with other cosmological constraints. The best-fit model has n = 0.91 −0.09 and Q10 = 18.0 −1.5 μK. Conditioning on n = 1 we obtain h = 0.55 +0.13 −0.19, Ωo = 0.70 with a lower limit Ωo > 0.58 and Q10 = 18.0 +1.4 −1.5 μK. The amplitude and position of the dominant peak in the best-fit power spectrum are Apeak = 76 +3 −7 μK and lpeak = 260 +30 −20. Unlike the Ωo = 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 < ∼ Ωo < ∼ 0.85. Using an approximate joint likelihood to combine our CMB constraint on Ωoh 1/2 with other cosmological constraints we obtain h = 0.58± 0.11 and Ωo = 0.65 +0.16 −0.15. Subject headings: cosmic microwave background – cosmology: observations Ap.J. , 496, in press (April 1, 1998) School of Physics, UNSW, Sydney 2052, Australia, [email protected] Observatoire de Strasbourg, 11 rue de l’Université, 67000 Strasbourg, France Centro de Astrof́ısica da U.P., Rua do Campo Alegre 823, 4150 Porto, Portugal