Towards realistic singularity-free cosmological models

We present an explicit general family of inhomogeneous cosmological models. The family contains an arbitrary function of comoving time (interpretable as the cosmological scale factor) and four arbitrary parameters. In general, it is a solution of Einstein's field equations for a fluid with anisotropic pressures, but it also includes a big subfamily of perfect-fluid metrics. The most interesting feature of this family is that it contains both all the diagonal separable singularity-free cosmological models recently found and all the Friedmann-Lemaitre-Robertson-Walker standard models. This property allows one to speculate on the construction of some interesting models in which the Universe has been FLRW-like from some time on (for instance, since the nucleosynthesis time), but it also went through primordial singularity-free inhomogeneous epochs (in fact, there are quite natural possibilities in which these primordial epochs are inflationary) without ever violating energy conditions or other physical properties. Nevertheless, the physical processes leading to the isotropization and homogenization of the Universe are not fixed nor indicated by the models themselves. The interesting properties of the general model are studied in some detail.