Redshift-distance relations from type Ia supernova observations. New constraints on grey dust models

Extinction due to intergalactic grey dust has been proposed as an alternative to accelerated expansion to account for the dimming of \s fluxes beyond $z \simeq 0.5$. The ``replenishing'' grey dust model, although fitting the observational data, does not seem to be based on physical assumptions. For this reason, in this paper we propose a new grey dust model whose dust distribution follows the comoving SFR density evolution, a reasonably established phenomenon. This new model is compared with the updated photometric data sample from the High Z Supernova Search Team (HZT). Also, using pairs of supernovae at different redshifts, the possibility of any ``patchy'' distribution proposed to explain the discrepancies between the ``high $z$'' dust model and the \s observations at very high redshift ($z \ge 0.9$) is ruled out. Finally, the data are compared with different models with and without dark energy and a best fit to a universe with adimensional parameters $\Omega_{\mathrm{m0}} = 0.31$ and $\Omega_{\mathrm{\Lambda 0}} = 0.69$ is obtained, from which an age of the universe of $t_{0} \simeq 14.6 \times 10^{9}$ years is derived. This age is compatible with the age of the globular clusters using an equation of state $\omega = -1$ and it obviates the need to resort to any kind of phantom energy.