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

TL;DR

This study investigates how inhomogeneities in the universe affect cosmological parameter constraints using supernovae and gamma-ray burst data within a Zeldovich-Kantowski-Dyer-Roeder framework, highlighting the impact on dark energy models.

Contribution

It introduces a combined analysis of supernovae and GRB data considering inhomogeneities via the smoothness parameter, refining constraints on matter density and dark energy.

Findings

Supernova data constrains matter density to about 0.27 with inhomogeneity consideration.

GRB data alone cannot tightly constrain the smoothness parameter.

Joint analysis yields tighter bounds on matter density and lower limits on smoothness.

Abstract

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.