Constraining the dark energy and smoothness parameter with type Ia Supernovae and Gamma-Ray Bursts

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 (ZKDR) approach which is phenomenologically characterized by a smoothness parameter $\alpha$, we rediscuss the constraints on the cosmic parameters based on Supernovae type Ia and Gamma-Ray Bursts (GRBs) data. The present analysis is restricted to a flat $\Lambda$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 (Amanullah {\it et al.} 2010) constrains the pair of parameters ($\Omega_m, \alpha$) to $\Omega_m=0.27_{-0.03}^{+0.08}$($2\sigma$) and $\alpha \geq 0.25$. A similar analysis based only on 59 Hymnium GRBs (Wei 2010) constrains the matter density parameter to be $\Omega_m= 0.35^{+0.62}_{-0.24}$ ($2\sigma$) while all values for the smoothness parameter are allowed. By performing a joint analysis, it is found that $\Omega_m = 0.27^{+0.06}_{-0.03}$ and $\alpha \geq 0.52$. 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.