V. C. Busti, R. C. Santos, J. A. S. Lima
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 generalized
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.
View original:
http://arxiv.org/abs/1202.0449
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