The integrated emission from γ rays formed by cosmic-ray interactions in star-forming galaxies will make a "guaranteed&" γ-ray background. Pavlidou & Fields [35] calculate this intensity by approximating the diffuse Galactic γ-ray spectrum as a broken power law and assuming that the γ-ray spectrum of a star-forming galaxy is proportional to the supernova rate and thus the massive star-formation rate, which can be inferred from the measured blue and UV luminosity density. Fig. 1a shows their results for a dust-corrected star formation rate (SFR) integrated over all redshifts, and a lower curve where the SFR is integrated to redshift unity.
A different approach
[46,
47]
to this problem starts by noting that cosmic-ray protons in the Milky
Way lose only 
10% of their energy before escaping. This fraction could rise to
nearly 100% in starburst galaxies where the target gas density is
much higher and the timescale for escape, due primarily to advective
galactic winds rather than diffusion in the galaxy's magnetic field,
is less than the nuclear loss time. Support for this contention is
provided by the observed correlation between far infrared
flux-primarily due to starlight reradiated by dust and gas-with
synchrotron flux produced by cosmic ray electrons. If both are
proportional to the supernova rate, and the radio-emitting electrons
lose a large fraction of their energy due to synchrotron cooling, then
this correlation is explained
[51].
The calculated intensity
[46]
from starburst galaxies is
shown in Fig. 1a. The bulk of this
intensity is formed at redshifts
1, where the
starburst fraction of star-forming galaxies is
large. The starburst intensity from Ref.
[46]
is smaller than the the total star-forming galaxy contribution
[35],
even when the latter calculation is truncated at z = 1. The latter
calculation was checked in Ref.
[14],
based on the
γ-ray
spectrum of the Milky Way. Stecker
[39]
argues that the starburst contribution is a factor
5 lower than diffuse
γ-ray and
neutrino intensity derived by Loeb and Waxman
[26]
and Thompson et al.
[46]
by pointing out that
directly accelerated electrons make a strong contribution to the
synchrotron flux, and questioning the assumption that protons lose all
their energy in starbursts. This criticism is addressed in
Ref.
[47].
GLAST will clarify this situation through its observations of nearby star-forming galaxies, e.g., LMC, SMC, M31, and M33, the starburst galaxies M82 and NGC 253, and infrared luminous galaxies like Arp 220. These galaxies are predicted to be GLAST sources [35, 48, 15, 46], and will provide benchmarks to correlate γ-ray fluxes with star formation activity.