Probing cosmic isotropy with Gamma-ray bursts: A dipole and quadrupole analysis of BATSE and Fermi GBM data

The cosmological principle, asserting large-scale homogeneity and isotropy, underpins the standard model of cosmology. Testing its validity using independent astronomical probes remains crucial for understanding the global structure of the Universe. We investigate the angular distribution of Gamma-Ray Bursts (GRBs) using two of the most comprehensive all-sky datasets available, the BATSE (CGRO) and Fermi GBM catalogs, to test the isotropy of the GRB sky at large angular scales. We perform spherical harmonic decomposition of the GRB sky maps and estimate the dipole and quadrupole amplitudes. Statistical significance is evaluated by comparing the observed multipole amplitudes against distributions derived from 500 Monte Carlo realizations of isotropic skies. Our results show that the observed dipole amplitudes for both BATSE and Fermi GBM datasets lie within the $1σ$ region of their respective null distributions. However, the quadrupole amplitude in the raw, uncorrected BATSE and Fermi GBM skies appears elevated at $3.7σ$ and $3.0σ$, respectively. After incorporating the BATSE sky exposure function, this apparent quadrupole anisotropy vanishes, indicating that instrumental non-uniformities fully account for the signal in that case. Owing to the absence of a publicly available full-sky exposure model for Fermi GBM, the Fermi analysis is restricted to the raw sky distribution. Our method’s reliability is validated through controlled simulations, which show it can detect the injected dipoles in BATSE-sized isotropic skies. These findings reinforce the statistical isotropy of the GRB sky and underscore the importance of accurate exposure corrections in cosmological anisotropy analyses.

💡 Research Summary

The paper investigates whether the large‑scale isotropy assumed in the standard cosmological model holds for the sky distribution of gamma‑ray bursts (GRBs). Using the two most extensive all‑sky GRB catalogs—BATSE (2702 bursts detected between 1991 and 2000) and Fermi GBM (4032 bursts detected from 2008 to 2025)—the authors perform a spherical‑harmonic analysis limited to the dipole (ℓ = 1) and quadrupole (ℓ = 2) moments. Positions are converted to Galactic coordinates and pixelised with HEALPix at Nside = 8 (768 equal‑area pixels). For each pixel the fluctuation f(θ, φ) =