  Recently, new observations of Li6 in Pop II stars of the galactic halo have
shown a surprisingly high abundance of this isotope, about a thousand times
higher than its predicted primordial value. In previous papers, a cosmological
model for the cosmic ray-induced production of this isotope in the IGM has been
developed to explain the observed abundance at low metallicity. In this paper,
given this constraint on the Li6, we calculate the non-thermal evolution with
redshift of D, Be, and B in the IGM. In addition to cosmological cosmic ray
interactions in the IGM, we include additional processes driven by SN
explosions: neutrino spallation and a low energy component in the structures
ejected by outflows to the IGM. We take into account CNO CRs impinging on the
intergalactic gas. Although subdominant in the galactic disk, this process is
shown to produce the bulk of Be and B in the IGM, due to the differential metal
enrichment between structures (where CRs originate) and the IGM. We also
consider the resulting extragalactic gamma-ray background which we find to be
well below existing data. The computation is performed in the framework of
hierarchical structure formation considering several star formation histories
including Pop III stars. We find that D production is negligible and that a
potentially detectable Be and B plateau is produced by these processes at the
time of the formation of the Galaxy (z ~ 3).
