The existence of inhomogeneities in the observed Universe modifies the distance-redshift relations thereby affecting the results of cosmological tests in comparison to the ones derived assuming spatially uniform models. By modeling the inhomogeneities through a Zeldovich-Kantowski-Dyer-Roeder approach which is phenomenologically characterized by a smoothness parameter $\alpha$, we rediscuss the constraints on the cosmic parameters based on type Ia supernovae (SNe Ia) and gamma-ray bursts (GRBs) data. The present analysis is restricted to a flat $\Lambda \mathrm{CDM}$ model with the reasonable assumption that $\Lambda$ does not clump. A ${\chi }^2$ analysis using 557 SNe Ia data from the Union2 compilation data (R. Amanullah et al., Astrophys. J. 716, 712 (2010).) constrains the pair of parameters (${\Omega }_m$, $\alpha$) to ${\Omega }_m={0.27}_{-0.03}^{+0.08}$ ($2\sigma$) and $\alpha \ge 0.25$. A similar analysis based only on 59 Hymnium GRBs (H. Wei, J. Cosmol. Astropart. Phys. 08 (2010) 020.) constrains the matter density parameter to be ${\Omega }_m={0.35}_{-0.24}^{+0.62}$ ($2\sigma$) while all values for the smoothness parameter are allowed. By performing a joint analysis, it is found that ${\Omega }_m={0.27}_{-0.03}^{+0.06}$ and $\alpha \ge 0.52$. As a general result, although considering that current GRB data alone cannot constrain the smoothness $\alpha$ parameter, our analysis provides an interesting cosmological probe for dark energy even in the presence of inhomogeneities.

Close

PrevNext

View figure in article

• 
• 
• 
•