Distributional cosmological quantities solve the paradox of soft singularity crossing

Both dark energy models and modified gravity theories could lead to cosmological evolutions different from either the recollapse into a Big Crunch or exponential de Sitter expansion. The newly arising singularities may represent true endpoints of the evolution or alternatively they can allow for the extension of geodesics through them. In the latter case only the components of the Riemann tensor representing tidal forces diverge. A subclass of these soft singularities, the Sudden Future Singularity (SFS) occurs at finite time, finite scale factor and finite Hubble parameter, only the deceleration parameter being divergent. In a Friedmann universe evolving in the framework of general relativity they are realized by perfect fluids with regular energy density and diverging pressure at the SFS. A particular SFS, the Big Brake occurs when the energy density vanishes and the expansion arrives at a full stop at the singularity. Such scenarios are generated by either a particular scalar field (the tachyon field) ...