A Cosmological Solution with Acceleration Caused by an Annihilation Shock Wave

Abstract

A discontinuous spherically symmetric solution of the Einstein equations is found, containing an annihilation shock wave. Before the shock wave, there occurs a parabolic (with zero speed at infinity) compression of dust consisting of particles and antiparticles, which is glued on the wave of complete annihilation of antiparticles with hyperbolic expansion of a gas with an extremely stiff equation of state. Specifically, in contrast to the Friedmann homogeneous expansion. the solution behind the shock wave has a nonzero pressure gradient associated with acceleration of the continuum. Estimates are given for the parameters related to the stage of baryon-antibaryon annihilation at formation of the Universe.