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 \chi ^ { 2 } 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 \ell = 10 .
Conditioning on \Omega _ { o } = 1 we obtain h = 0.33 \pm 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 \pm 0.10 .
We quote \Delta \chi ^ { 2 } = 1 contours as error bars , however because of nonlinearities of the models , these may be only crude approximations to 1 \sigma confidence limits .

A favored open model with \Omega _ { o } = 0.3 and h = 0.70 is more than \sim 4 \sigma from the CMB data best-fit model and is rejected by goodness-of-fit statistics at the 99 \% CL .
High baryonic models ( \Omega _ { b } h ^ { 2 } \sim 0.026 ) yield the best CMB \chi ^ { 2 } fits and are more consistent with other cosmological constraints .
The best-fit model has n = 0.91 ^ { +0.29 } _ { -0.09 } and Q _ { 10 } = 18.0 ^ { +1.2 } _ { -1.5 } \mu K. Conditioning on n = 1 we obtain h = 0.55 ^ { +0.13 } _ { -0.19 } , \Omega _ { o } = 0.70 with a lower limit \Omega _ { o } > 0.58 and Q _ { 10 } = 18.0 ^ { +1.4 } _ { -1.5 } \ > \mu K. The amplitude and position of the dominant peak in the best-fit power spectrum are A _ { peak } = 76 ^ { +3 } _ { -7 } \mu K and \ell _ { 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 \mbox { $\ > \stackrel { < } { { } _ { \sim } } \ > $ } \Omega _ { o } \mbox { $\ > \stackrel { < } { { } _ { % \sim } } \ > $ } 0.85 .
Using an approximate joint likelihood to combine our CMB constraint on \Omega _ { o } h ^ { 1 / 2 } with other cosmological constraints we obtain h = 0.58 \pm 0.11 and \Omega _ { o } = 0.65 ^ { +0.16 } _ { -0.15 } .

Subject headings : cosmic microwave background – cosmology : observations