2.7. Conclusions on H₀

The progress in determining the extragalactic distance scale has been dramatic. The ladders yield values convergent within 10%, which is compared to a factor 1.6 disagreement in the early nineties. A new uncertainty, however, becomes manifest in the Galactic distance scale: there is a 15-20% uncertainty in the distance to LMC. Therefore, we may summarise

(10)

as a currently acceptable value of the Hubble constant. This agrees with that from HST-KP (Mould et al. 1999) up to the uncertainty from the LMC distance, though we followed a different path of argument. This allows H₀ = 90 at the high end (if Tonry et al's SBF is weighted) and 60 at the low end (if the SNeIa results are weighted). Note that H₀ from both EPM and gravitational lensing are consistent with the ladder value for (m - M)_LMC = 18.5. With the shorter LMC distance the overlap is marginal.

The short LMC distance will also cause trouble for the H₀-age consistency. The LMC distance modulus of m - M = 18.25 would raise the lower limit of H₀ to 72, and increase the lower limit of age from 11.5 Gyr to 14.5 Gyr at the same time. There is then no solution for a = 0 universe. With a non-zero , a unique solution is H₀ 72, 0.25, 0.75 with coeval globular cluster formation (see Figure 6 below).

In the future it is likely that more effort will be expended for geometric methods. The great advantage is that it is free from errors arising from the chemical composition. In the surface brightness method, the chemical composition may still enter into the game, but its effect is tolerable and can even be reduced to a negligible level by using near infrared observations.

Ultimately, gravitational wave observations could provide us with a novel method. For instance, for coalescing binary neutron stars the distance can be calculated as d ~ ^{-2 -1 -1}, where is metric perturbations, is the frequency and = / is a characteristic time of the collapse (Schutz 1986). The position of the object may be difficult to infer, but there might be a gamma ray burst associated with the coalescence.