Modified temperature redshift relation and UHECR propagation

We re-examine the interactions of ultra-high energy cosmic rays (UHECRs) with photons from the cosmic microwave background (CMB) under a changed, locally non-linear temperature redshift relation $T(z)$. This changed temperature redshift relation is motivated by the postulate of subjecting thermalised and isotropic photon gases such as the CMB to an SU(2) rather than a U(1) gauge group. This modification of $\Lambda$CDM is called SU(2)$_{\rm CMB}$, and some cosmological parameters obtained by SU(2)$_{\rm CMB}$ seem to be in better agreement with local measurements of the same quantities. In this work, we apply the reduced CMB photon density under SU(2)$_{\rm CMB}$ to the propagation of UHECRs. This leads to a higher UHECR flux just below the ankle in the cosmic ray spectrum and slightly more cosmogenic neutrinos under otherwise equal conditions for emission and propagation. Most prominently, the proton flux is significantly increased below the ankle ($5\times10^{18}$ eV) for hard injection spectra and without considering the effects of magnetic fields. The reduction in CMB photon density also favours a decreased cosmic ray source evolution than the best fit using $\Lambda$CDM. In consequence, it seems that SU(2)$_{\rm CMB}$ favours sources that evolve as the star formation rate (SFR), like star burst galaxies (SBG) and gamma ray bursts (GRB), over active galactic nuclei (AGNs) as origins of UHECRs. We conclude that the question about the nature of primary sources of UHECRs is tightly-knit with the actual temperature redshift relation of the CMB.