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Cosmic rays are appealing as a source of ionization in starburst galaxiesbecause of the great columns they can penetrate, but in the densest regions ofstarbursts, they may be stopped by pion production and ionization energylosses. I argue that gamma rays are the source of ionization in the deepestmolecular clouds of dense starbursts, creating Gamma-Ray Dominated Regions(GRDRs). Gamma rays are not deflected by magnetic fields, have a luminosity upto ~1/3 that of the injected cosmic rays, and can easily penetrate columndepths of ~100 g/cm^2 before being attenuated by gamma-Z pair production. Theionization rates of GRDRs, <~10^-16 s^-1, are much smaller than in cosmic raydominated regions, but in the most extreme starbursts, they may still reachvalues comparable to those in Milky Way molecular clouds. The gas temperaturesin GRDRs could be likewise low, <~10 K if there is no additional heating fromdust or turbulence, while at high densities, the kinetic temperature willapproach the dust temperature. The ratio of ambipolar diffusion time tofree-fall time inside GRDRs in dense starbursts is expected to be similar tothose in Milky Way cores, suggesting star-formation can proceed normally inthem. The high columns of GRDRs may be opaque even to millimeter wavelengths,complicating direct studies of them, but I argue that they could appear asmolecular line shadows in nearby starbursts with ALMA. Since GRDRs are cold,their Jeans masses are not large, so that star-formation in GRDRs may have anormal or even bottom-heavy initial mass function.

Gamma-Ray Dominated Regions: Extending the Reach of Cosmic Ray Ionization in Starburst Environments