Lorentz Invariance Violation and the Observed Spectrum of Ultrahigh Energy Cosmic Rays

TL;DR

This paper investigates how small violations of Lorentz invariance could affect the spectrum of ultrahigh energy cosmic rays, comparing theoretical predictions with recent experimental data to constrain the possible extent of LIV.

Contribution

It provides a detailed calculation of LIV effects on the UHECR spectrum and compares these with recent observations to set upper limits on LIV parameters.

Findings

Best fit LIV parameter of approximately 4.5 x 10^{-23}

LIV could cause a recovery in the cosmic ray spectrum at higher energies

Current data is consistent with a small but nonzero LIV effect

Abstract

There has been much interest in possible violations of Lorentz invariance, particularly motivated by quantum gravity theories. It has been suggested that a small amount of Lorentz invariance violation (LIV) could turn off photomeson interactions of ultrahigh energy cosmic rays (UHECRs) with photons of the cosmic background radiation and thereby eliminate the resulting sharp steepening in the spectrum of the highest energy CRs predicted by Greisen Zatsepin and Kuzmin (GZK). Recent measurements of the UHECR spectrum reported by the HiRes and Auger collaborations, however, indicate the presence of the GZK effect. We present the results of a detailed calculation of the modification of the UHECR spectrum caused by LIV using the formalism of Coleman and Glashow. We then compare these results with the experimental UHECR data from Auger and HiRes. Based on these data, we find a best fit amount of LIV of $4.5^{+1.5}_{-4.5} \times 10^{-23}$,consistent with an upper limit of $6 \times 10^{-23}$. This possible amount of LIV can lead to a recovery of the cosmic ray spectrum at higher energies than presently observed. Such an LIV recovery effect can be tested observationally using future detectors.