  The aim of this paper is to check if the models with realistic inhomogeneous
matter distribution and without cosmological constant can explain the dimming
of the supernovae in such a way that it can be interpreted as an acceleration
of the Universe. Employing the simplest inhomogeneous model, i.e.
Lemaitre-Tolman model, this paper examines the impact of inhomogeneous matter
distribution on light propagation. These analyses show that realistic matter
fluctuations on small scales induce brightness fluctuations in the residual
Hubble diagram of amplitude around 0.15 mag, and thus can mimic acceleration.
However, it is different on large scales. All these brightness fluctuations
decrease with distance and hence cannot explain the dimmining of supernovae for
high redshift without without invoking the cosmological constant.This paper
concludes that models with realistic matter distribution (i.e. where variation
of the density contrast is similar to what is observed in the local Universe)
cannot explain the observed dimming of supernovae without the cosmological
constant.
