Constraints on leptonically annihilating Dark Matter from reionization and extragalactic gamma background

The PAMELA, Fermi and HESS experiments (PFH) have shown anomalous excesses in the cosmic positron and electron fluxes. A very exciting possibility is that those excesses are due to annihilating dark matter (DM). In this paper we calculate constraints on leptonically annihilating DM using observational data on diffuse extragalactic gamma-ray background and measurements of the optical depth to the last-scattering surface, and compare those with the PFH favored region in the m_{DM} - <\sigma_A v> plane. Having specified the detailed form of the energy input with PYTHIA Monte Carlo tools we solve the radiative transfer equation which allows us to determine the amount of energy being absorbed by the cosmic medium and also the amount left over for the diffuse gamma background. We find that the constraints from the optical depth measurements are able to rule out the PFH favored region fully for the \tau^{-}+\tau^{+} annihilation channel and almost fully for the \mu^{-}+\mu^{+} annihilation channel. It turns out that those constraints are quite robust with almost no dependence on low redshift clustering boost. The constraints from the gamma-ray background are sensitive to the assumed halo concentration model and, for the power law model, rule out the PFH favored region for all leptonic annihilation channels. We also find that it is possible to have models that fully ionize the Universe at low redshifts. However, those models produce too large free electron fractions at z > ~100 and are in conflict with the optical depth measurements. Also, the magnitude of the annihilation cross-section in those cases is larger than suggested by the PFH data.