Non-linear structure formation and 'apparent' acceleration: an investigation

We present an analytically tractable non-linear model of structure formation in a Universe with only dust. The model is a Lema (i) over cap tre-Tolman-Bondi solution (of general relativity) and structures are shells of different density. We show that the luminosity distance-redshift relation has significant corrections at low redshift when the density contrast becomes non-linear. A minimal effect is a correction in apparent magnitudes of order Delta m similar or equal to 0.15. We discuss different possibilities that could further enhance this effect and mimic dark energy.