© CAMBRIDGE UNIVERSITY PRESS 1999

1.4 Measuring ₀

1.4.1 Very Large Scale Measurements

Although it would be desirable to measure ₀ and through their effects on the large-scale geometry of space-time, this has proved difficult in practice since it requires comparing objects at higher and lower redshift, and it is hard to separate selection effects or the effects of the evolution of the objects from those of the evolution of the universe. For example, Kellermann (1993), using the angular-size vs. redshift relation for compact radio galaxies, obtained evidence favoring 1; however, selection effects may invalidate this approach (Dabrowski, Lasenby, & Saunders 1995). To cite another example, in ``redshift-volume'' tests (e.g. Loh & Spillar 1986) involving number counts of galaxies per redshift interval, how can we tell whether the galaxies at redshift z ~ 1 correspond to those at z ~ 0? Several galaxies at higher redshift might have merged, and galaxies might have formed or changed luminosity at lower redshift. Eventually, with extensive surveys of galaxy properties as a function of redshift using the largest telescopes such as Keck, it should be possible to perform classical cosmological tests at least on particular classes of galaxies - that is one of the goals of the Keck DEEP project.

At present, perhaps the most promising technique involves searching for Type Ia supernovae (SNe Ia) at high-redshift, since these are the brightest supernovae and the spread in their intrinsic brightness appears to be relatively small. Perlmutter et al. (1996) have recently demonstrated the feasibility of finding significant numbers of such supernovae, but a dedicated campaign of follow-up observations of each one is required in order to measure ₀ by determining how the apparent brightness of the supernovae depends on their redshift. This is therefore a demanding project. It initially appeared that ~ 100 high redshift SNe Ia would be required to achieve a 10% measurement of q₀ = ₀ / 2 - . However, using the correlation mentioned earlier between the absolute luminosity of a SN Ia and the shape of its light curve (slower decline correlates with higher peak luminosity), it now appears possible to reduce the number of SN Ia required. The Perlmutter group has now analyzed seven high redshift SN Ia by this method, with the result for a flat universe that ₀ = 1- = 0.94^+0.34_-0.28, or equivalently = 0.06^+0.28_-0.34 (< 0.51 at the 95% confidence level) (Perlmutter et al. 1996). For a = 0 cosmology, they find ₀ = 0.88^+0.69_-0.60. In November 1995 they discovered an additional 11 high-redshift SN Ia, and they have subsequently discovered many more. Other groups, collaborations from ESO and MSSSO/CfA/CTIO, are also searching successfully for high-redshift supernovae to measure ₀ (Garnavich et al. 1996). There has also been recent progress understanding the physical origin of the SN Ia luminosity-light curve correlation, and in discovering other such correlations. At the present rate of progress, a reliable answer may be available within perhaps a year or two if a consensus emerges from these efforts.