Testing Isotropic Universe Using the Gamma-Ray Burst Data of Fermi / GBM
  The sky distribution of Gamma-Ray Bursts (GRBs) has been intensively studied
by various groups for more than two decades. Most of these studies test the
isotropy of GRBs based on their sky number density distribution. In this work
we propose an approach to test the isotropy of the Universe through inspecting
the isotropy of the properties of GRBs such as their duration, fluences and
peak fluxes at various energy bands and different time scales. We apply this
method on the {\em Fermi} / Gamma-ray Burst Monitor (GBM) data sample
containing 1591 GRBs. The most noticeable feature we found is near the Galactic
coordinates $l\approx 30^\circ$, $b\approx 15^\circ$ and radius $r\approx
20^\circ-40^\circ$. The inferred probability for the occurrence of such an
anisotropic signal (in a random isotropic sample) is derived to be less than a
percent in some of the tests while the other tests give results consistent with
isotropy. These are based on the comparison of the results from the real data
with the randomly shuffled data samples. Considering large number of statistics
we used in this work (which some of them are correlated to each other) we can
anticipate that the detected feature could be result of statistical
fluctuations. Moreover, we noticed a considerably low number of GRBs in this
particular patch which might be due to some instrumentation or observational
effects that can consequently affect our statistics through some systematics.
Further investigation is highly desirable in order clarify about this result,
e.g. utilizing a larger future {\em Fermi} / GBM data sample as well as data
samples of other GRB missions and also looking for possible systematics.
