Péridier Library Abstract Archive

Abstract No. UT 376

Title: Likely Value of the Cosmological Constant
Author(s): Hugo Martel, Paul R. Shapiro, and Steven Weinberg
Keywords: cosmology: theory --- galaxies: formation
E-Mail: Hugo Martel (to request a full copy of this paper)
Preprint: 9701046 Document source or PostScript
Release date: 01/22/97 09:14:08
Publication status: submitted to Astrophysical Journal, in press
Comments: 57 13 pages, 11 1 figures

In theories in which the cosmological constant Lambda takes a variety of values in different "subuniverses," the probability distribution of its observed values is conditioned by the requirement that there must be someone to measure it. This probability is proportional to the fraction of matter which is destined to condense out of the background into mass concentrations large enough to form observers. We calculate this "collapsed fraction" by a simple, pressure-free, spherically symmetric, nonlinear model for the growth of density fluctuations in a flat universe with arbitrary value of the cosmological constant, applied in a statistical way to the observed spectrum of density fluctuations at recombination. From this, the probability distribution for the vacuum energy density rho_V = Lambda/8pi G for Gaussian random density fluctuations is derived analytically. It is shown that the results depend on only one quantity, sigma³ RHO, where sigma² and RHO are the variance and mean value of the fluctuating matter density field at recombination, respectively. To calculate sigma, we adopt the flat CDM model with nonzero cosmological constant and fix the amplitude and shape of the primordial power spectrum in accordance with data on cosmic microwave background anisotropy from the COBE satellite DMR experiment. A comparison of the results of this calculation of the likely values of rho_V with present observational bounds on the cosmological constant indicates that the small, positive value of rho_V (up to 3 times greater than the present cosmic mass density) suggested recently by several lines of evidence is a reasonably likely value to observe, even if all values of rho_V are equally likely a priori. Recent work has shown that the speed of the cooling front in soft X-ray transients may be an important clue in understanding the nature of accretion disk viscosity. In a previous paper (Vishniac and Wheeler 1996) we derived the scaling law for the cooling front speed. Here we derive a similarity solution for the hot inner part of disks undergoing cooling. This solution is exact in the limit of a thin disk, power law opacities, and a minimum hot state column density which is an infinitesimal fraction of the maximum cold state density. For a disk of finite thickness the largest error is in the ratio of the mass flow across the cooling front to the mass flow at small radii. Comparison to the numerical simulations of Cannizzo et al. (1995) indicates that the errors in other parameters do not exceed ( c_sF / r_F Omega_F )^q, that is, the ratio of the sound speed at the disk midplane to its orbital velocity, evaluated at the cooling front, to the qth power. Here q approx 1/2. Its precise value is determined by the relevant hot state opacity law and the functional form of the dimensionless viscosity.