Simple inhomogeneous cosmological (toy) models
  Based on the Lema\^itre-Tolman-Bondi (LTB) metric we consider two flat
inhomogeneous big-bang models. We aim at clarifying, as far as possible
analytically, basic features of the dynamics of the simplest inhomogeneous
models and to point out the potential usefulness of exact inhomogeneous
solutions as generalizations of the homogeneous configurations of the
cosmological standard model. We discuss explicitly partial successes but also
potential pitfalls of these simplest models. Although primarily seen as toy
models, the relevant free parameters are fixed by best-fit values using the
Joint Light-curve Analysis (JLA)-sample data. On the basis of a likelihood
analysis we find that a local hump with an extension of almost 2 Gpc provides a
better description of the observations than a local void for which we obtain a
best-fit scale of about 30 Mpc. Future redshift-drift measurements are
discussed as a promising tool to discriminate between inhomogeneous
configurations and the $\Lambda$CDM model.
