Testing the homogeneity of the Universe using gamma-ray bursts^⋆

¹ Institute of Astronomy and Space Science, Sun Yat-Sen University, 510275 Guangzhou, PR China
e-mail: limh@ihep.ac.cn; linhn@ihep.ac.cn
² Department of Physics, Chongqing University, 401331 Chongqing, PR China

Received: 26 January 2015
Accepted: 29 July 2015

Abstract

Aims. The discovery of a statistically significant clustering in the distribution of gamma-ray bursts (GRBs) has recently been reported. Given that the cluster has a characteristic size of 2000–3000 Mpc and a redshift between 1.6 ≤ z ≤ 2.1, it has been claimed that this structure is incompatible with the cosmological principle of homogeneity and isotropy of our Universe. 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.

Methods. 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, ξ(r), is calculated using a Landy-Szalay estimator. We perform a standard least-χ² 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 r³ within 1%, or equivalently above which the correlation dimension of the sample D₂ is within 1% of D₂ = 3.

Results. For a flat ΛCDM Universe, a best-fit power law, ξ(r) = (r/r₀)^{− γ}, with the correlation length r₀ = 413.64 ± 135.40 h^-1 Mpc and slope γ = 1.57 ± 0.63 (at 1σ confidence level) for the real-space correlation function ξ(r) is obtained. We obtain a homogeneous distribution of GRBs with correlation dimension above D₂ = 2.97 on scales of r ≥ 8200 h^-1 Mpc. For the Swift subsample of 244 GRBs, the correlation length and slope are r₀ = 387.51 ± 132.75 h^-1 Mpc and γ = 1.57 ± 0.65 (at 1σ confidence level). The corresponding scale for a homogeneous distribution of GRBs is r ≥ 7700 h^-1 Mpc. For the 75 SHOALS GRBs, the results are are r₀ = 288.13 ± 192.85 h^-1 Mpc and γ = 1.27 ± 0.54 (at 1σ confidence level), with the homogeneity scale r ≥ 8300 h^-1 Mpc. For the 113 SHOALS GRBs at 0 < z < 6.3, the results are r₀ = 489.66 ± 260.90 h^-1 Mpc and γ = 1.67 ± 1.07 (at 1σ confidence level), with the homogeneity scale r ≥ 8700 h^-1 Mpc.

Conclusions. 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.