Title: Fuzzy Bounces

Abstract: We observe that the energy and the enthalpy densities can be smeared by two fudge factors that are constrained by the contracted Bianchi identities. Depending on the smearing functions the underlying cosmological solutions belong to two complementary (but physically different) classes, namely the bounces of the scale factor and the curvature bounces. Gradient instabilities and singularities may appear in the evolution of curvature inhomogeneities and this general conclusion is corroborated by the concrete examples associated with different forms of the smearing functions. While the backgrounds obtained in this manner might seem technically regular, the evolution of the curvature inhomogeneities restrict the ranges of the solutions that turn out to be unsuitable even for a limited description of the pre-inflationary initial data. It is however not excluded that a class of scenarios (mainly associated with the curvature bounces) could indeed avoid the potential instabilities.