The cosmic gamma-ray background in the MeV range

The $\gamma$-ray background from supernovae is calculated on the basis of the reconstructed efficiency of supernova explosions from star formation at various redshifts. The calculations presented here show how Type Ia SN rates compatible with the results of optical supernova searches give a background emission in the MeV range that can explain the extragalactic emission measured by COMPTEL and SMM. Star formation histories reaching maximum values of 0.3-0.4 M$_{\odot}$ yr$^{-1}$ Mpc$^{-3}$ at z$\sim$ 1.5 (and/or possibly keeping that value to higher z) give a $\gamma$-ray background compatible with observations while they also predict the observed supernova rates per comoving volume. The $\gamma$-ray background in the MeV range is mostly sensitive to the star formation rate at z$\sim$ 1-2, but the activity in forming stars at even higher z has an influence as well on the absolute level of the cosmic $\gamma$-ray background: the time elapsed by the SNe Ia progenitors until they explode has a broad distribution and the rates of SNe Ia at z$\sim$ 1.5-2 depend on the formation frequencies of their progenitor stars at earlier epochs. The mutual consistency of predictions of optical rates and integrated emission in the $\gamma$-ray domain place in a firm ground the Type Ia supernova identification as the astrophysical source responsible for this cosmic background