Understand
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 (ZKDR) luminosity distance redshift relation for a flat ($\Lambda$CDM) model.
- A $\chi^{2}$-analysis using the 115 SNe Ia data of Astier {\it 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 $\in [0,1]$ are allowed even at 1$\sigma$).