The Ups and Downs of the Hubble Constant

A brief history of the determination of the Hubble constant H_0 is given. Early attempts following Lemaitre (1927) gave much too high values due to errors of the magnitude scale, Malmquist bias and calibration problems. By 1962 most authors agreed that 75< H_0 <130. After 1975 a dichotomy arose with values near 100 and others around 55. The former came from apparent-magnitude-limited samples and were affected by Malmquist bias. New distance indicators were introduced; they were sometimes claimed to yield high values of H_0, but the most recent data lead to H_0 in the 60's, yet with remaining difficulties as to the zero-point of the respective distance indicators. SNe Ia with their large range and very small luminosity dispersion (avoiding Malmquist bias) offer a unique opportunity to determine the large-scale value of H_0. Their maximum luminosity can be well calibrated from 10 SNe Ia in local parent galaxies whose Cepheids have been observed with HST. An unforeseen difficulty - affecting all Cepheid distances - is that their P-L relation varies from galaxy to galaxy, presumably in function of metallicity. A proposed solution is summarized here. The conclusion is that H_0 = 63.2 +/- 1.3 (random) +/- 5.3 (systematic) on all scales. The expansion age becomes then (with Omega_m=0.3, Omega_Lambda=0.7) 15.1 Gyr.Comment: 30 pages, 12 figures, 2 tables. 79th Annual Scientific Meeting of the Astronomische Gesellschaft 2005, Karl-Schwarzschild-Lecture, to appear in Reviews in Modern Astronomy, 19,

The mystery of the cosmic vacuum energy density and the accelerated expansion of the Universe

After a short history of the $\Lambda$-term it is explained why the (effective) cosmological constant is expected to obtain contributions from short-distance-physics, corresponding to an energy scale of at least 100 GeV. The actual tiny value of the cosmological constant in any natural scale of units represents, therefore, one of the deepest mysteries of present day fundamental physics. We also briefly discuss recent astronomical evidence for a cosmologically significant vacuum energy density causing an accelerating expansion of the universe. This arises mainly from the Hubble diagram of type Ia supernovae and from the observed temperature fluctuations of the cosmic microwave background radiation. If this should become an established fact, we are also confronted with a disturbing {\it cosmic coincidence} problem.Comment: 12 pages, 2 figures, iopart macros include

Stable Solution of the Simplest Spin Model for Inverse Freezing

We analyze the Blume-Emery-Griffiths model with disordered magnetic interaction that displays the inverse freezing phenomenon. The behavior of this spin-1 model in crystal field is studied throughout the phase diagram and the transition and spinodal lines for the model are computed using the Full Replica Symmetry Breaking Ansatz that always yields a thermodynamically stable phase. We compare the results both with the formulation of the same model in terms of Ising spins on lattice gas, where no reentrance takes place, and with the model with generalized spin variables recently introduced by Schupper and Shnerb [Phys. Rev. Lett. {\bf 93} 037202 (2004)], for which the reentrance is enhanced as the ratio between the degeneracy of full to empty sites increases. The simplest version of all these models, known as the Ghatak-Sherrington model, turns out to hold all the general features characterizing an inverse transition to an amorphous phase, including the right thermodynamic behavior.Comment: 4 pages, 4 figure