511 keV line and diffuse gamma rays from moduli

We obtain the spectrum of gamma-ray emissions from the moduli whose decay into e(+)e(-) accounts for the 511 keV line observed by SPI/INTERGRAL. The moduli emit gamma rays through internal bremsstrahlung, and also decay directly into two gammas via tree and/or one-loop diagrams. We show that the internal bremsstahlung constrains the mass of the moduli below similar to 40 MeV model-independently. On the other hand, the flux of two gammas directly decayed from the moduli through one-loop diagrams will exceed the observed galactic diffuse gamma-ray background if the moduli mass exceeds similar to 20 MeV in the typical situation. Moreover, forthcoming analysis of SPI data in the range of 1-8 MeV may detect the line emisson with the energy half the moduli mass in the near future, which confirms the decaying moduli scenario.