  Recently, the PAMELA, FERMI, HESS, and ATIC instruments have discovered
interesting spectral features in the positron to total electron ratio and in
the total electronic component of cosmic rays at high energy. These
observations are studied with analytical models for the propagation of cosmic
rays emanating from a discrete set of sources or from a smooth distribution of
sources extending over the Galaxy. The contrast between the theoretically
expected spectra from these two source distributions is seen to play a crucial
role in the interpretation of the recent findings. It is shown that the
positron to electron ratio, observed by PAMELA, may be fit over the entire
energy range in the nested leaky-box model for cosmic ray propagation and that
the ratio is expected to reach an asymptotic value of $\sim0.6$ at high
energies in all conventional models of cosmic ray propagation. We also derive
the spectral shape of the electrons and positrons expected from the
annihilation of dark matter in the Galaxy and show that the spectral shape of
the peak will provide important information, not only regarding the mass of the
dark matter particles, but also regarding their spatial distribution. The
spectrum of secondary positrons and electrons, calculated with the nested
leaky-box model, is subtracted from the spectrum of the electronic component to
determine the spectrum of primary electrons emerging from the cosmic ray
sources. This spectrum is analyzed in terms of contributions from a set of
discrete sources sprinkled across the Galactic volume. Our analysis suggests
the possible presence of electrons, accelerated in high Mach number shocks, in
the cosmic rays.

Cosmology and Nongalactic Astrophysics