Abstract:
We propose a method for testing isotropy of a three-dimensional distribution using Shannon
entropy. We test the method on some Monte Carlo simulations of isotropic and anisotropic
distributions and find that the method can effectively identify and characterize different types
of hemispherical asymmetry inputted in a distribution. We generate anisotropic distributions
by introducing pockets of different densities inside homogeneous and isotropic distributions
and find that the proposed method can effectively quantify the degree of anisotropy and
determine the geometry of the pockets introduced. We also consider spherically symmetric
radially inhomogeneous distributions which are anisotropic at all points other than the centre
and find that such anisotropy can be easily characterized by our method. We use a semi analytic galaxy catalogue from the Millennium simulation to study the anisotropies induced
by the redshift space distortions and find that the method can separate such anisotropies from
a general one. The method may be also suitably adapted for any two-dimensional maps on the
celestial sphere to study the hemispherical asymmetry in other cosmological observations
