A CONVENIENT SET OF COMOVING COSMOLOGICAL VARIABLES AND THEIR APPLICATION

A set of cosmological variables, which we shall refer to as 'supercomo ving variables', are presented which are an alternative to the standar d comoving variables, particularly useful for describing the gas dynam ics of cosmic structure formation. For an ideal gas with a ratio of sp ecific heats gamma = 5/3, the supercomoving position, velocity and the rmodynamic properties (i.e, density, temperature and pressure) of matt er are constant in time in a uniform, isotropic, adiabatically expandi ng universe. Expressed in terms of these supercomoving variables, the non-relativistic, cosmological fluid conservation equations of the New tonian approximation and the Poisson equation closely resemble their n on-cosmological counterparts. This makes it possible to generalize non -cosmological results and techniques to address problems involving dep artures from uniform, adiabatic Hubble expansion in a straightforward way, for a wide range of cosmological models. These variables were ini tially introduced by Shandarin to describe structure formation in matt er-dominated models. In this paper, we generalize supercomoving variab les to models with a uniform contribution to the energy density corres ponding to a non-zero cosmological constant, domain walls, cosmic stri ngs, a non clumping form of non-relativistic matter (e.g. massive neut rinos in the presence of primordial density fluctuations of small wave length) 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 p arameter Omega(X0) of the additional non-clumping component. For each type of non-clumping background, we identify families within which dif ferent values of Omega(0) and Omega(X0) lead to fluid equations and so lutions in supercomoving variables which are independent of the cosmol ogical parameters Omega(0) and Omega(X0),. We also generalize the desc ription to include the effects of non-adiabatic processes such as heat ing, radiative cooling, thermal conduction and viscosity, as well as m agnetic fields in the MHD approximation. As an illustration, we descri be three familiar cosmological problems in supercomoving variables: th e growth of linear density fluctuations, the non-linear collapse of a 1D plane-wave density fluctuation leading to pancake formation, and th e well-known Zel'dovich approximation for extrapolating the linear gro wth of density fluctuations in three dimensions to the non-linear stag e.