Cosmological Parameters

The discussion of cosmological parameters used to be a source of embarrassment to cosmologists. Today, measurements of the cosmological parameters are leading the way into the era of precision cosmology. The CMB temperature is measured to four significant figures, T_0=2.7277+/-0.002 K; the Hubble constant is now determined with a reliable error estimate, H_0=(65+/-5) km sec^-1 Mpc^-1; the mass density of baryons is precisely determined by big-bang nucleosynthesis Omega_B = (0.019+/-0.001) h^-2; and the age of the Universe inferred from the ages of the oldest stars is 14+/-1.5 Gyr, which is consistent the expansion age. Further, we have the first full accounting of matter and energy in the Universe, complete with a self consistency check. Expressed as a fraction of the critical density it goes like this: neutrinos, between 0.3% and 15%; stars, between 0.3% and 0.6%; baryons (total), 5+/-0.5%; matter (total),40% +/- 10%; smooth, dark energy, 80% +/- 20%; totaling to the critical density (within the errors).Comment: 27 pages LaTeX with 8 eps figures. To be published in The Proceedings of Particle Physics and the Universe (Cosmo-98), edited by David O. Caldwell (AIP, Woodbury, NY

Measuring subdiffusion parameters

We propose a method to extract from experimental data the subdiffusion parameter $\alpha$ and subdiffusion coefficient $D_\alpha$ which are defined by means of the relation $=2D_\alpha/\Gamma(1+\alpha) t^\alpha$ where $$ denotes a mean square displacement of a random walker starting from $x=0$ at the initial time $t=0$. The method exploits a membrane system where a substance of interest is transported in a solvent from one vessel to another across a thin membrane which plays here only an auxiliary role. Using such a system, we experimentally study a diffusion of glucose and sucrose in a gel solvent. We find a fully analytic solution of the fractional subdiffusion equation with the initial and boundary conditions representing the system under study. Confronting the experimental data with the derived formulas, we show a subdiffusive character of the sugar transport in gel solvent. We precisely determine the parameter $\alpha$, which is smaller than 1, and the subdiffusion coefficient $D_\alpha$.Comment: 17 pages, 9 figures, revised, to appear in Phys. Rev.