  Recent results from the CoGeNT collaboration (as well as the annual
modulation reported by DAMA/LIBRA) point toward dark matter with a light (5-10
GeV) mass and a relatively large elastic scattering cross section with nucleons
(\sigma ~ 10^{-40} cm^2). In order to possess this cross section, the dark
matter must communicate with the Standard Model through mediating particles
with small masses and/or large couplings. In this Letter, we explore with a
model independent approach the particle physics scenarios that could
potentially accommodate these signals. We also discuss how such models could
produce the gamma rays from the Galactic Center observed in the data of the
Fermi Gamma Ray Space Telescope. We find multiple particle physics scenarios in
which each of these signals can be accounted for, and in which the dark matter
can be produced thermally in the early Universe with an abundance equal to the
measured cosmological density.

High Energy Physics - Phenomenology;Cosmology and Nongalactic Astrophysics;High Energy Astrophysical Phenomena