Shock Waves and Cosmology

which satisfies Einstein’s equations of general relativity with a perfect fluid source. In this model, which accounts for things on the largest length scale, the universe is approximated by a space of uniform density and pressure at each fixed time, and the expansion rate is determined by the cosmological scale factor R(t) that evolves according to the Einstein equations. Astronomical observations show that the galaxies are uniform on a scale of about one billion lightyears, and the expansion is critical – that is, k = 0 in (1) – and so, according to (1), on the largest scale, the universe is infinite flat Euclidean space R3 at each fixed time. Here R(t) determines the Hubble “constant”, H(t) = Ṙ(t)/R(t) and c/H(t) is called the Hubble distance at time t > 0, (c is the speed of light). In the standard model, the Hubble constant, which measures the recessional velocity of the galaxies, applies to the entire universe of infinite mass and extent, at each time t > 0. That is, the entire universe burst out from the Big-Bang at t = 0, and the universe is of infinite mass and extent at each time t > 0. In order to avoid this seemingly unphysical situation, we have been exploring the possibility of a new cosmological model, in which the expansion of the galaxies is a bounded expansion of finite total mass. In our model, the FRW universe emerges from the Big-Bang with a shock wave at the leading edge of the expansion, analogous to a classical shock wave explosion. In order to close the resulting Einstein equations, we take as equation of state