  Measurements of the diffuse extragalactic gamma-ray background (EGRB) are
complicated by a strong Galactic foreground. Estimates of the EGRB flux and
spectrum, obtained by modeling the Galactic emission, have produced a variety
of (sometimes conflicting) results. The latest analysis of the EGRET data found
an isotropic flux I_x=1.45+-0.05 above 100 MeV, in units of 10^-5 s^-1 cm^-2
sr^-1. We analyze the EGRET data in search for robust constraints on the EGRB
flux, finding the gamma-ray sky strongly dominated by Galactic foreground even
at high latitudes, with no conclusive evidence for an additional isotropic
component. The gamma-ray intensity measured towards the Galactic poles is
similar to or lower than previous estimates of I_x. The high latitude profile
of the gamma-ray data is disk-like for 40<|b[deg]|<70, and even steeper for
|b|>70; overall it exhibits strong Galactic features and is well fit by a
simple Galactic model. Based on the |b|>40 data we find that I_x<0.5 at a 99%
confidence level, with evidence for a much lower flux. We show that
correlations with Galactic tracers, previously used to identify the Galactic
foreground and estimate I_x, are not satisfactory; the results depend on the
tracers used and on the part of the sky examined, because the Galactic emission
is not linear in the Galactic tracers and exhibits spectral variations across
the sky. The low EGRB flux favored by our analysis places stringent limits on
extragalactic scenarios involving gamma-ray emission, such as radiation from
blazars, intergalactic shocks and production of ultra-high energy cosmic rays
and neutrinos. We suggest methods by which future gamma-ray missions such as
GLAST and AGILE could indirectly identify the EGRB.
