Propagation of jump discontinuities in relativistic cosmology

A recent dynamical formulation at a derivative level ${\partial }^{3}g$ for fluid spacetime geometries $(\mathcal{M},\mathbf{g},\mathbf{u}),$ that employs the concept of evolution systems in a first-order symmetric hyperbolic format, implies the existence in the Weyl curvature branch of a set of timelike characteristic three-surfaces associated with the propagation speed $|v|=\frac{1}{2}$ relative to fluid-comoving observers. We show it is a physical role of the constraint equations to prevent realization of jump discontinuities in the derivatives of the related initial data so that Weyl curvature modes propagating along these three-surfaces cannot be activated. In addition we introduce a new, illustrative first-order symmetric hyperbolic evolution system at a derivative level ${\partial }^{2}g$ for baryotropic perfect fluid cosmological models that are invariant under the transformation of an Abelian $G_2$ isometry group.