Massless particle diffusion in causal set theory

Particles propagating in a fundamentally discrete spacetime will not follow the smooth geodesics predicted by general relativity. In causal set theory we can construct a simple Lorentz invariant model for the 'swerving' of massive particles caused by discreteness. On macroscopic scales these swerves can be approximated by a diffusion equation in phase space. For massless particles a model is less simple to construct, but a diffusion equation can still be obtained. We find that massless particles will undergo a diffusion and drift in momentum magnitude. This effect will be most significant over cosmic distances. The diffusion and drift distorts a blackbody spectrum, and thus the perfect blackbody nature of the cosmic microwave background allows us to place tight constraints on the values of the diffusion and drift constants.