Supernova Ia observations in the Lema tre-Tolman model

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. Lema tre-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. PACS Codes: 98.65.Dx, 98.65.-r, 98.62.Ai