Concepts of Optimality and Their Uses

Lecture to the memory of Alfred Nobel, December 11, 1975allocation of resources;

Gravitational Lens Time Delays in CDM

In standard CDM halo models, the time delay of a gravitational lens is determined by the cold baryon mass fraction, f, of the visible galaxy relative to the overall halo. The observed time delays in PG1115+080, SBS1520+530, B1600+434 and HE2149-2745 give Hubble constants consistent with the HST Key Project value of H0=72+/-8 km/s Mpc only if f>0.2 (1-sided 68% confidence), which is larger than the upper bound of fmax=Omega_b/Omega_0=0.15+/-0.05 estimated from the CMB. If all available baryons cool and f=fmax then the time delays imply H0=65+/-6 km/s Mpc (95% confidence). If local inventories of cold baryons, f=0.013/h70, are correct, then H0=52+/-6 km/s Mpc and the halo parameters closely match isothermal mass models. Isothermal models are also consistent with strong and weak lens studies, stellar dynamics and X-ray observations on these scales, while significantly more centrally concentrated models are not. There is a a conflict between gravitational lens time delays, the local distance scale and standard CDM halo models.Comment: Submitted to ApJ. 22 pages, 7 figure