Cosmic Radiation Constraints on Low String Scale and Extra Dimension Cross Sections

The observed interaction energy of cosmic rays with atmospheric nuclei reaches up to a PeV in the center of mass. We compute nucleon-nucleon and nucleon-neutrino cross sections for various generic parton cross sections appearing in string and brane world scenarios for gravity and compare them with cosmic ray data. Scenarios with effective energy scales in the TeV range and parton cross sections with linear or stronger growth with the center of mass energy appear strongly constrained or ruled out. String-inspired scenarios with infinite-volume extra dimensions may require a fundamental scale above 100 eV for which they are probably in conflict with gravity on parsec scales.