A convenient set of comoving cosmological variables and their application

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 an ideal gas with a ratio of specific heats γ = 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 non-relativistic, cosmological fluid conservation equations of the Newtonian approximation and the Poisson equation closely resemble their non-cosmological counterparts. This makes it possible to generalize non-cosmological 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 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 non-zero cosmological constant, domain walls, cosmic strings, a non-clumping form of non-relativistic 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 Ω0 of the non-relativistic matter component in which density fluctuation is possible, and the density parameter ΩX0 of the additional non-clumping component. For each type of non-clumping background, we identify families within which different values of Ω0 and ΩX0 lead to fluid equations and solutions in supercomoving variables which are independent of the cosmological parameters Ω0 and ΩX0. We also generalize the description to include the effects of non-adiabatic 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 non-linear collapse of a 1D 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 non-linear stage.