Cosmic Rays Report from the Structure of Space

Figure 1

Flux of cosmic rays multiplied by is reproduced from published data (see text for references) without recalibration for unbiased assessment by the principle of least action. Coloring merely serves to emphasize various spectral regions. Comparison of data with the computed flux (orange line) via (5) indicates that most particles below 10^15.6 eV, known as the “knee,” have departed from sources in the expanding Universe, whereas above the “knee” the calculated flux from a stationary system with the characteristic (green dashed line) via (3) implies that recorded particles originate from sources in the nearby nonexpanding part of the Universe. The close match of computed flux with data at the “knee” provides an estimate for the radius  Mpc (with ±10% uncertainty shown by grey lines) of the nonexpanding part of the Universe. Above the knee the flux decreases as because protons will slow down first by producing photons and eventually neutrinos (green line). Then, above 10^17.2 eV, known as the “2nd knee,” the flux decreases as because protons will slow down more effectively producing pairs of electrons and positrons (blue line), and then above 10^19.6 eV the flux decreases approximately as , known as the GZK cutoff, by the even more effective pion production (purple line). The decelerated protons by various mechanisms will return to lower energies. The reflux from the meson production (violet line) will give rise to the “ankle” at about 10^18.6 eV above which the flux decreases as and likewise the reflux from the lepton production (dark green) will give rise to the “bow” at about 10^16.4 eV above which the flux decreases as .