The Future of H₀ from Gravitational Lensing

For the three CLASS GL systems discussed above (Sect.2), the time delays are or will soon be known with errors less than 10%. With the ongoing efforts to improve the determination of the lens potentials of each individual GL system, in particular those from B0218+357 and B1608+656 (Sect.3), one might also expect the uncertainty on the inferred time delays to reduce to less than 10% in the near future, although as indicated this still requires a considerable effort. These systems will then give an average global value of H₀ comparable in accuracy to the results from the HST Key-Project. Together with other GL systems that have measured time delays, this situation can only improve. Another example of a very promising CLASS GL system is B1933+503 (Sykes et al. 1998), for which the inferred time delay from mass modeling has an uncertainty 20%, with excellent opportunities for improvement (Cohn et al. 2000; see also Nair 1998). Although no time delay could be determined from a VLA monitoring campaign (Biggs et al. 2000), the source has in the past varied by as much as 33% at 15 GHz and is currently being re-observed with both the VLA and MERLIN. To increase the number of GL systems with measured time delays, CLASS is now engaged in two new monitoring projects with the VLA (8 systems; PI: Fassnacht) and MERLIN (Key-Programme; 8-12 systems; PI: Koopmans). In total 14 different CLASS GL systems will be monitored (including two of those in Sect.2). With ongoing optical monitoring programs, the total number of GL systems being monitored in 2001 will likely be 20-30! Although not every system will yield time delays, we expect that the number of GL systems with measured time delays is likely to double in the next few years.

However, in order to obtain a `competitive' global measurement of H₀ from gravitational lensing, the focus in the coming years needs to be on improving the determination of the deflector potential of each individual GL system from which time delays are being measured. From the work being done at present, this appears to be a difficult, but certainly not an unattainable goal. In light of the fact that the first GL system was discovered over twenty years ago, progress might appear slow. However, the first unambiguous measurement of a time delay was done only some five years ago and since then at least seven GL systems have been added to this list, some of them having much simpler deflector potentials than Q0957+561, which has received the most attention over the last two decades.

Finally, we can ask ourselves the question: Is it still worthwhile to measure H₀ from gravitational lensing, now that the HST Key-Project has determined the local value with an uncertainty of around 10%? Here, one should keep in mind that the value of H₀ determined from gravitational lensing is a `global' single-step determination, whereas that determined from the HST Key-Project is a `local' (distance-ladder) value. The HST Key-Project has measured distances out to 400Mpc (z0.1; e.g. Freedman et al. 2001), whereas the typical gravitational lens/source (angular-diameter) distances are 1500-2000Mpc. Both methods are therefore in some sense complementary and do not necessarily have to result in the same value for the expansion speed of the universe (i.e. locally H₀ could differ from its global average value). This is often implicitly assumed based on the idea that the universe is homogeneous and isotropic on very large scales (but not necessarily on smaller scales), although recent work has indicated that the ratio of the global over the local value of H₀ probably does not deviate from unity by more than a few percent (see Freedman et al. 2001 for a discussion). Homogeneity implies the R-W metric and a set of global parameters describing the evolution of the universe (i.e. the Friedmann equations), which by definition implies the same local and global value of H₀. Agreement or disagreement between values of H₀ from two or more independent and different methods over a wide range of distances (i.e. redshifts) can therefore elucidate our understanding of the universe and in case of agreement put its determination on a much firmer basis.

© Copyright Astronomical Society of Australia 1997