Hydrodynamic self-similar cosmological models

TL;DR

This paper generalizes hydrodynamic self-similar solutions by introducing new variables, providing a systematic method to obtain solutions, and presenting Newtonian analogs of all homogeneous isotropic Friedmann dust universes with different spatial curvatures.

Contribution

It introduces a systematic procedure for deriving hydrodynamic self-similar solutions and extends the class of solutions to include Newtonian analogs of Friedmann dust universes.

Findings

Generalized self-similar solutions using new variables.

Provided Newtonian analogs for all homogeneous isotropic Friedmann dust universes.

Established a systematic method for solution derivation.

Abstract

Hydrodynamic self-similar solutions, as obtained by Chi [J. Math. Phys. 24, 2532 (1983)] have been generalized by introducing new variables in place of the old space and time variables. A systematic procedure of obtaining a complete set of solutions has been suggested. The Newtonian analogs of all homogeneous isotropic Friedmann dust universes with spatial curvature $k = 0, \pm 1$ have been given.