Low energy bounds on Poincaré violation in causal set theory

In the causal set approach to quantum gravity, Poincaré symmetry is modified by swerving in spacetime, induced by the random lattice discretization of the spacetime structure. The broken translational symmetry at short distances is argued to lead to a residual diffusion in momentum space, whereby a particle can acquire energy and momentum by drift along its mass shell and a system in equilibrium can spontaneously heat up. We consider bounds on the rate of momentum space diffusion coming from astrophysical molecular clouds, nuclear stability and cosmological neutrino background. We find that the strongest limits come from relic neutrinos, which we estimate to constrain the momentum space diffusion constant by $k<{10}^{-61}{\mathrm{GeV}}^3$ for neutrinos with masses $m_{\nu }>0.01\mathrm{eV}$, improving the previously quoted bounds by roughly 17 orders of magnitude.