Probing the Dark Dimension with Auger data

[Abridged] By combining swampland conjectures with observational data, it was recently noted that our universe could stretch off in an asymptotic region of the string landscape of vacua. In this framework, the cosmological hierarchy problem can be resolved by the addition of one mesoscopic (dark) dimension of size $\sim \lambda \, \Lambda^{-1/4} \sim 1~\mu{\rm m}$. The Planck scale of the higher dimensional theory, $M_{\rm UV} \sim \lambda^{-1/3} \Lambda^{1/12} M_{\rm Pl}^{2/3} \sim 10^{10}~{\rm GeV}$, is tantalizingly close to the energy above which the TA and Auger collaborations found conclusive evidence for a sharp cutoff of the flux of UHECRs. It was recently suggested that since physics becomes strongly coupled to gravity beyond $M_{\rm UV}$, universal features deep-rooted in the dark dimension could control the energy cutoff of the source spectra. Conversely, in the absence of phenomena inborn within the dark dimension, we would expect a high variance of the cosmic ray maximum energy characterizing the source spectra, reflecting the many different properties inherent to the most commonly assumed UHECR accelerators. A recent analysis of Auger and TA data exposed strong evidence for a correlation between UHECRs and nearby starburst galaxies, with a global significance post-trial of $4.7\sigma$. Since these galaxies are in our cosmic backyard, the flux attenuation factor due to cosmic ray interactions en route to Earth turns out to be negligible. This implies that for each source, the shape of the observed spectrum should roughly match the emission spectrum, providing a unique testing ground for the dark dimension hypothesis. Using Auger data, we carry out a maximum likelihood analysis to characterize the shape of the UHECR emission from the galaxies dominating the anisotropy signal. We show that the observed spectra could be universal only if $\lambda \lesssim 10^{-3}$.