Old high-redshift galaxies and primordial density fluctuation spectra

We have discovered a population of extremely red galaxies at $z\simeq 1.5$ which have apparent stellar ages of \gs 3 Gyr, based on detailed spectroscopy in the rest-frame ultraviolet. In order for galaxies to have existed at the high collapse redshifts indicated by these ages, there must be a minimum level of power in the density fluctuation spectrum on galaxy scales. This paper compares the required power with that inferred from other high-redshift populations. If the collapse redshifts for the old red galaxies are in the range $z_c\simeq 6$ -- 8, there is general agreement between the various tracers on the required inhomogeneity on 1-Mpc scales. This level of small-scale power requires the Lyman-limit galaxies to be approximately $\nu\simeq 3.0$ fluctuations, implying a very large bias parameter $b\simeq 6$. The high collapse redshifts of the red galaxies as deduced from gravitational collapse provides independent support for the ages estimated from their stellar populations. Such early-forming galaxies are rare, and their contribution to the cosmological stellar density is consistent with an extrapolation to higher redshifts of the star-formation rate measured at $z<5$; there is no evidence for a general era of spheroid formation at extreme redshifts.Comment: 9 Pages MNRAS in press. Uses MNRAS Plain TeX macro

Sub and Super-Luminal Propagation of Intense Pulses in Media with Saturated and Reverse Absorption

We develop models for the propagation of intense pulses in solid state media which can have either saturated absorption or exhibit reverse absorption . We show that the experiments of Bigelow {\it et al.}[Phys. Rev. Lett. {\bf 90}, 113903 (2003); Science {\bf 301}, 200 (2003).] on subluminal propagation in Ruby and superluminal propagation in Alexandrite are well explained by modelling them as three level and four level systems coupled to Maxwell equations. We present results well beyond the traditional pump-probe approach.Comment: 4 pages, 6 figure