Constraining the dark energy and smoothness parameter with supernovae

The presence of inhomogeneities modifies the cosmic distances through the gravitational lensing effect, and, indirectly, must affect the main cosmological tests. Assuming that the dark energy is a smooth component, the simplest way to account for the influence of clustering is to suppose that the average evolution of the expanding Universe is governed by the total matter-energy density whereas the focusing of light is only affected by a fraction of the total matter density quantified by the alpha Dyer-Roeder parameter. By using two different samples of SNe type Ia data, the Omega(m) and alpha parameters are constrained by applying the Zeldovich-Kantowski-Dyer-Roeder luminosity distance-redshift relation for a flat (Lambda CDM) model. Lambda chi(2)-analysis using the 115 SNe Ia data of the Astier et al. sample (2006) constrains the density parameter to be Omega(m)=0.26(-0.07)(+0.17) (2 sigma) while the alpha parameter is weakly limited (all the values is an element of[0,1] are allowed even at 1 sigma). However, a similar analysis based the 182 SNe Ia data of Riess et al. (2007) constrains the pair of parameters to be Omega(m)=0.33(-0.07)(+0.09) and alpha >= 0.42 (2 sigma). Basically, this occurs because the Riess et al. sample extends to appreciably higher redshifts. As a general result, even considering the existence of inhomogeneities as described by the smoothness alpha parameter, the Einstein-de Sitter model is ruled out by the two samples with a high degree of statistical confidence (11.5 sigma and 9.9 sigma, respectively). The inhomogeneous Hubble-Sandage diagram discussed here highlights the necessity of the dark energy, and a transition deceleration/accelerating phase at z similar to 0.5 is also required.