Supernovae Ia observations in the Lemâitre–Tolman model

The observation of distant supernovae shows 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 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. The luminosity distance obtained in inhomogeneous models can be slightly different from FLRW models. Employing the simplest inhomogeneous model, i.e. Lemâitre–Tolman model, this paper examines the impact of an inhomogeneous matter distribution on light propagation. Recent studies in this field proved that matter inhomogeneities can mimic the acceleration. Our analyses show that realistic matter fluctuations on small scales introduce the brightness fluctuation in the residual Hubble diagram of amplitude δm ≈ 0.15 mag, and thus can mimic the acceleration. However on large scales the situation differ. All these brightness fluctuations decrease for high redshifts, which can explain why nearby supernovae are of larger intrinsic dispersion than distant ones. This, however, does not explain the excess of faint supernovae. This paper concludes that there is no realistic model which could explain the observed dimming of supernovae without a cosmological constant.