Testing the homogeneity of the Universe using gamma-ray bursts

Abstract

In this paper, we study the homogeneity of the GRB distribution using a subsample of the Greiner GRB catalogue, which contains 314 objects with redshift $0<z<2.5$ (244 of them discovered by the Swift GRB Mission). We try to reconcile the dilemma between the new observations and the current theory of structure formation and growth. To test the results against the possible biases in redshift determination and the incompleteness of the Greiner sample, we also apply our analysis to the 244 GRBs discovered by Swift and the subsample presented by the Swift Gamma-Ray Burst Host Galaxy Legacy Survey (SHOALS). The real space two-point correlation function (2PCF) of GRBs, $\xi(r),$ is calculated using a Landy-Szalay estimator. We perform a standard least-$\chi^2$ fit to the measured 2PCFs of GRBs. We use the best-fit 2PCF to deduce a recently defined homogeneity scale. The homogeneity scale, $R_H$, is defined as the comoving radius of the sphere inside which the number of GRBs $N(<r)$ is proportional to $r^3$ within $1\%$, or equivalently above which the correlation dimension of the sample $D_2$ is within $1\%$ of $D_2=3$. For the Swift subsample of 244 GRBs, the correlation length and slope are $r_0= 387.51 \pm 132.75~h^{-1}$Mpc and $\gamma = 1.57\pm 0.65$ (at $1\sigma$ confidence level). The corresponding scale for a homogeneous distribution of GRBs is $r\geq 7,700~h^{-1}$Mpc. The results help to alleviate the tension between the new discovery of the excess clustering of GRBs and the cosmological principle of large-scale homogeneity. It implies that very massive structures in the relatively local Universe do not necessarily violate the cosmological principle and could conceivably be present.