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 type Ia Supernovae ( SNe 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 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 can not constrain the smoothness \alpha parameter our analysis provides an interesting cosmological probe for dark energy even in the presence of inhomogeneities .