Strong shock in a uniform expanding universe. Approximate and exact solutions of self-similar equations

TL;DR

This paper derives both approximate and exact self-similar solutions for the propagation of a strong shock in a flat, expanding universe, comparing their accuracy and exploring conditions for solutions with different equations of state.

Contribution

It provides the first exact numerical solutions for strong shocks in an expanding universe, extending previous approximate analytic models.

Findings

Exact solutions closely match approximate ones, especially away from the shock.

Differences are most significant near the shock front.

Self-similar solutions are limited to narrower parameter ranges for polytropic gases.

Abstract

Self-similar solution is obtained for propagation of a strong shock, in a flat expanding dusty Friedman universe. Approximate analytic solution was obtained earlier, using relation between self-similar variables, equivalent to the exact energy conservation integral, which was obtained by L.I. Sedov for the strong explosion in the static uniform medium. Numerical integration of self-similar equation is made here, giving an exact solution of the problem, which is rather close to the approximate analytic one. The differences between these solutions are most apparent in the vicinity of the shock. For polytropic equation of state, self-similar solutions exist in more narrow interval of the adiabatic power than in the static case.