Were we to choose at random a hundred members of the IAU and ask each of them to tell us the value of the Hubble constant and how it is measured, few if any would refer to gravitational lens time delay measurements. Most would instead refer to observations of Cepheid variables with HST or to observations of the CMB power spectrum with WMAP. These set the de facto standard against which time delay estimates must be evaluated.
The Cepheids give a Hubble constant of 72 km/s/Mpc with a 10% uncertainty [Freedman et al. (2001)], a result that most of our randomly chosen astronomers would find relatively straightforward. But only a handful of them would be able to tell us how the CMB power spectrum yields a measurement of the Hubble constant.
In his opening talk, David SPERGEL told us that three numbers are determined to high accuracy by the CMB power spectrum: the height of the first peak, the contrast between the heights of the even and odd peaks, and the distance between peaks. Ask anyone who calls himself a cosmologist how many free parameters his world model has and the number N will be larger than three. Spergel's three numbers constrain combinations of those N parameters, but do not, in particular, tightly constrain the Hubble constant. One must supplement the CMB either with observations, or alternatively, with non-observational constraints.
The effects of supplementing the observed CMB power spectrum with other observations, and of adopting (or declining to adopt) non-observational constraints, are shown in table 1. All of the numbers shown are taken from the analysis by [Tegmark et al. (2004b)]. They use the first year data from the Wilkinson Microwave Anisotropy Probe [Bennett et al. (2003)], the second data release of the Sloan Digital Sky Survey [Abazajian et al. (2004)], the [Tonry et al. (2003)], data for high redshift Type Ia supernovae, and data from 6 other CMB experiments: Boomerang, DASI, MAXIMA, VSA, CBI and ACBAR.
| very-nearly flat | perfectly flat | ||||
| observations |  tot |
100h | observations | tot |
100h |
| WMAP1 | 1.086+0.057-0.128 | 50+16-13 | WMAP1 | 1 | 74+18-7 |
| add SDSS2 | 1.058+0.039-0.041 | 55+9-6 | add SDSS2 | 1 | 70+4-3 |
| add SNae | 1.054+0.048-0.041 | 60+9-6 | add other CMB | 1 | 69+3-3 |
We see from the first line of table 1 that the
value of
the Hubble constant derived from the WMAP1 data alone is a factor of
1.5 or 2.5 more uncertain than the Cepheid result, depending upon
whether the universe is taken to be perfectly flat or only very-nearly
flat. Combining the galaxy power spectrum as measured with SDSS2
[Tegmark et
al. (2004a)]
reduces the
uncertainties by factors of 3 and 2, respectively. In the very-nearly
flat case, adding type Ia supernovae does little to change the
uncertainty but shifts the value of H0 closer to the
Cepheid value.
In the perfectly flat case, adding other CMB measurements reduces the
uncertainty in H0 by another factor of 1.3. Small
deviations from flatness produce substantial changes in the Hubble
constant, with the product
htot5 remaining roughly constant
[Tegmark et al. (2004b)].
Suppose we were to show table 1 to our randomly
chosen IAU
members and again ask them the value of the Hubble constant (and its
uncertainty). Some would argue that the results for the very-nearly
flat case are so very-nearly flat that it is reasonable to adopt
perfect flatness as a working model. We observe that
| logtot|
< 0.10, when it might have been of order 100 (or
perhaps 3 if one admits anthropic reasoning). But others would be
reluctant to take perfect flatness for granted. The very sensitivity
of the Hubble constant to that assumption would be an argument against
adopting it. The present author is, himself, ambivalent.