Peridier Library Abstract Archive

Abstract No. UT 394

Title: A Convenient Set of Comoving Cosmological Variables and their Application
Author(s): Hugo Martel and Paul R. Shapiro
Keywords: cosmology: theory --- dark matter --- galaxies: intergalactic medium --- hydrodynamics --- large-scale structure of universe
Email: Hugo Martel (to request a full copy of this paper)
Preprint: 9710119 Document source or PostScript
Release date: 03/03/98 13:45:51
Publication status: M.N.R.A.S., in press (1998)
Comments: 38 pages, 2 figures

A set of cosmological variables, which we shall refer to as "supercomoving variables," are presented which are an alternative to the standard comoving variables, particularly useful for describing the gas dynamics of cosmic structure formation. For ideal gas with a ratio of specific heats gamma=5/3, the supercomoving position, velocity, and thermodynamic properties (i.e. density, temperature, and pressure) of matter are constant in time in a uniform, isotropic, adiabatically expanding universe. Expressed in terms of these supercomoving variables, the nonrelativistic, cosmological fluid conservation equations of the Newtonian approximation and the Poisson equation closely resemble their noncosmological counterparts. This makes it possible to generalize noncosmological results and techniques to address problems involving departures from uniform, adiabatic Hubble expansion in a straightforward way, for a wide range of cosmological models. These variables were initially introduced by Shandarin (1980) to describe structure formation in matter-dominated models. In this paper, we generalize supercomoving variables to models with a uniform contribution to the energy density corresponding to a nonzero cosmological constant, domain walls, cosmic strings, a nonclumping form of nonrelativistic matter (e.g. massive neutrinos in the presence of primordial density fluctuations of small wavelength), or a radiation background. Each model is characterized by the value of the density parameter Omega_0 of the non-relativistic matter component in which density fluctuation is possible, and the density parameter Omega_X0 of the additional, nonclumping component. For each type of nonclumping background, we identify families within which different values of Omega_0 and Omega_X0 lead to fluid equations and solutions in supercomoving variables which are independent of the cosmological parameters Omega_0 and Omega_X0. We also generalize the description to include the effects of nonadiabatic processes such as heating, radiative cooling, thermal conduction and viscosity, as well as magnetic fields in the MHD approximation.

As an illustration, we describe three familiar cosmological problems in supercomoving variables: the growth of linear density fluctuations, the nonlinear collapse of a one-dimensional plane-wave density fluctuation leading to pancake formation, and the well-known Zel'dovich approximation for extrapolating the linear growth of density fluctuations in three dimensions to the nonlinear stage.