The contribution of Galactic TeV pulsar wind nebulae to Fermi-LAT diffuse emission

The large-scale diffuse $\gamma-$ray flux observed by Fermi-LAT in the 1-100 GeV energy range, parameterized as $\propto E^{-\Gamma}$, has a spectral index $\Gamma$ that depends on the distance from the Galactic center. This feature, if attributed to the diffuse emission produced by cosmic rays (CR) interactions with the interstellar gas, can be interpreted as the evidence of a progressive CR spectral hardening towards the Galactic center. This interpretation challenges the standard cosmic rays diffusion paradigm. We report on the implications of TeV Pulsar Wind Nebulae observed by the HESS Galactic Plane Survey in the 1-100 TeV energy range for the interpretation of Fermi-LAT data. We argue that a relevant fraction of this population cannot be resolved by Fermi-LAT in the GeV domain providing a relevant contribution to the large-scale diffuse emission, viz. the $30\%$ of the total diffuse $\gamma$-ray emission in the inner Galaxy. This additional component naturally accounts for a large part of the spectral index variation observed by Fermi-LAT, weakening the evidence of CR spectral hardening in the inner Galaxy.