Joining conditions for cosmological perturbations at an equation-of-state transition

Joining conditions for cosmological spatial irregularities at an equation-of-state transition spatial hypersurface are derived by requiring that the relativistic linear perturbation theory equations of motion remain singularity-free at the transition spatial hypersurface. The transition spatial hypersurface is taken to be a spatially homogeneous local energy-density spatial hypersurface, between two spacetime-dependent "speed-of-sound" fluid-dominated epochs of a spatially flat Friedmann-Lema\^{}tre-Robertson-Walker cosmological model. Since the spacetime-dependent "speed-of-sound" fluid model includes, as special cases, both the scalar field model and the ideal fluid model, these joining conditions may be used at the scalar-field-radiation and radiation-baryon transitions in simple inflation-modified hot big-bang models. These joining conditions differ from two earlier sets of joining conditions (which differ from each other).