Spherical Harmonic Expansion of Gamma‐Ray Burst Distributions: Probing Large‐Scale Structure?

We have laid down the formalism and techniques necessary for computing themultipole components in a spherical harmonic expansion for bursting sourcesgiven any specific power spectrum of density perturbations. Using thisformalism we have explicitly computed and tabulated the expected first fewmultipole components for the GRB distribution using a Cold Dark Matter powerspectrum. Unfortunately, our analysis leads us to expect that an anisotropysignal for this model of structure formation will be below the shot noise levelfor the foreseeable future. Earlier studies by others had claimed that it maybe possible within a decade or so to probe structure formation using theangular distribution of GRBs. We find that while it may be possible to probethe dipole due to our motion with respect to the cosmic rest-frame, it does notseem feasible to probe the multipole components due to intrinsic fluctuationsif the actual power spectrum is fixed to within an order of magnitude by theCold Dark Matter model of structure formation.