Abstract
We present an analytically tractable non-linear model of structure formation in a Universe
with only dust. The model is a Lemaître–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 
. We discuss different possibilities that could further enhance this effect and mimic dark
energy.