Angular correlations of the MeV cosmic gamma-ray background

The measured cosmic gamma-ray background (CGB) spectrum at MeV energies is in reasonable agreement with the predicted contribution from Type Ia supernovae (SNe Ia). However, the characteristic features in the SN Ia gamma-ray spectrum, weakened by integration over source redshifts, are difficult to measure, and the contributions from other sources in the MeV range are uncertain, so that the SN Ia origin of the MeV CGB remains unproven. Since different CGB sources have different clustering properties and redshift distributions, by combining the CGB spectrum and angular correlation measurements the contributions to the CGB could be identified and separated. The SN Ia CGB large-scale structure follows that of galaxies. Its rms fluctuation at degree scales has a characteristic energy dependence ranging from similar to1% to on the order of unity and can be measured to several percent precision by proposed future satellites such as the Advanced Compton Telescope. With the identification of the SN Ia contribution, the SN Ia rate could be measured unambiguously as a function of redshift up to z similar to 1 by combining the spectrum and angular correlation measurements, yielding new constraints on the star formation rate to even higher redshifts. Finally, we show that the gamma-ray and neutrino backgrounds from supernovae should be closely connected, allowing an important consistency test from the measured data. Identification of the astrophysical contributions to the CGB would allow much greater sensitivity to an isotropic high-redshift CGB contribution arising in extra dimension or dark matter models.