Supernova Ia observations in the Lemâitre–Tolman model

Observations of distant supernovae show that the light of supernovae Ia is dimmer than it would be in a decelerating universe. Several effects might be responsible for this phenomenon: cosmological constant, evolution of supernovae, selection bias, gravitational lensing, intergalactic dust, and influence of inhomogeneous distribution of matter on light propagation. All of these effects but the last one have been systematically studied and, except for the cosmological constant, according to the present knowledge they are not responsible for the observed dimming of supernovae. However, matter distribution in the Universe is not homogeneous. A luminosity distance obtained in inhomogeneous models can be slightly different from a distance provided by FLRW models. Employing the simplest inhomogeneous model, i.e. Lemâitre–Tolman model, this paper examines the impact of inhomogeneous matter distribution on light propagation. Recent studies in this field proved that matter inhomogeneities can mimic acceleration. These analyses show that realistic matter fluctuations on small scales induce brightness fluctuations in the residual Hubble diagram of amplitude δm ≈ 0.15 mag, and thus can mimic acceleration. However, it is different on large scales. All these fluctuations decrease with distance and hence cannot explain the dimmining of supernovae for high redshift. This paper concludes that there is no realistic model which could explain the observed dimming of supernovae without the cosmological constant.