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 $α$, 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 $Λ$CDM model with the reasonable assumption that $Λ$ does not clump. A $χ^{2}$-analysis using 557 SNe Ia data from the Union2 Compilation Data (Amanullah {\it et al.} 2010) constrains the pair of parameters ($Ω_m, α$) to $Ω_m=0.27_{-0.03}^{+0.08}$($2σ$) and $α\geq 0.25$. A similar analysis based only on 59 Hymnium GRBs (Wei 2010) constrains the matter density parameter to be $Ω_m= 0.35^{+0.62}_{-0.24}$ ($2σ$) while all values for the smoothness parameter are allowed. By performing a joint analysis, it is found that $Ω_m = 0.27^{+0.06}_{-0.03}$ and $α\geq 0.52$. As a general result, although considering that current GRB data alone cannot constrain the smoothness $α$ parameter our analysis provides an interesting cosmological probe for dark energy even in the presence of inhomogeneities.

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