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The slope of the locally measured spectrum of cosmic rays varies from 2.8 forprotons with energies below 200 GeV down to 2.5 for heavy nuclei with energiesin the TeV-PeV range. It is not clear if the locally measured slope values arerepresentative for those of the overall population of Galactic cosmic rays andif the slope of the cosmic ray spectrum varies across the Galaxy. We use thedata of Fermi Space gamma-ray Telescope to derive a measurement of the slope ofthe cosmic ray spectrum across the Galactic Disk and to compare it with that ofthe Large Magellanic Cloud cosmic rays. A special choice of the backgroundestimation regions allows us to single out the neutral pion decay component ofthe gamma-ray flux in the energy range above 10 GeV and to separate it from (a)emission from the local interstellar medium around the Solar system and (b)from the inverse Compton emission produced by cosmic ray electrons. Results.The spectrum of the pion decay gamma-ray emission from the Galactic disk in theenergy band 10 GeV - 1 TeV has the slope 2.4. There is no evidence for thevariation of the slope with Galactic longitude / distance from the GalacticCentre. The slope of the spectrum of cosmic rays derived from the gamma-raydata, 2.45, is harder than the slope of the locally observed cosmic ray protonspectrum. Pion decay emission from a powerlaw distribution of cosmic rays withthe same hard slope also provides a fit to the gamma-ray spectrum of the LargeMagellanic Cloud. Identical and hard slopes of the spectra of cosmic rays inthe Milky Way and in the Large Magellanic Cloud are consistent with astraightforward theoretical model in which cosmic rays are injected by shockacceleration with the spectrum with the slope 2...2.1 which is subsequentlymodified by 1/3...1/2 by the energy-dependent escape of cosmic rays through theturbulent Galactic magnetic field.

Hard spectrum of cosmic rays in the Disks of Milky Way and Large Magellanic Cloud