  Most of the diffuse Galactic GeV gamma-ray emission is produced via
collisions of cosmic ray (CR) protons with ISM protons. As such the observed
spectra of the gamma-rays and the CRs should be strongly linked. Recent
observations of Fermi-LAT exhibit a hardening of the gamma-ray spectrum at
around a hundred GeV, between the Sagittarius and Carina tangents, and a
further hardening at a few degrees above and below the Galactic plane. However,
standard CR propagation models that assume a time independent source
distribution and a location independent diffusion cannot give rise to a
spatially dependent CR (and hence gamma-ray) spectral slopes. Here we consider
a dynamic spiral arm model in which the distribution of CR sources is
concentrated in the (dynamic) spiral arms, and we study the effects of this
model on the $\pi^0$-decay produced gamma-ray spectra. Within this model, near
the Galactic arms the observed gamma-ray spectral slope is not trivially
related to the CR injection spectrum and energy dependence of the diffusion
coefficient. We find unique signatures that agree with the Fermi-LAT
observations. This model also provides a physical explanation for the
difference between the local CR spectral slope and the CR slope inferred from
the average gamma-ray spectrum.
