Quantum Gravity Phenomenology without Lorentz Invariance Violation: a detailed proposal

We describe a scheme for the exploration of quantum gravity phenomenology focussing on effects that could be thought as arising from a fundamental granularity of space-time. In contrast with the simplest assumptions, such granularity is assumed to respect Lorentz Invariance but is otherwise left unspecified. The proposal is fully observer covariant, it involves non-trivial couplings of curvature to matter fields and leads to a well defined phenomenology. We present the effective Hamiltonian which could be used to analyze concrete experimental situations, some of which are briefly described, and we shortly discuss the degree to which the present proposal is in line with the fundamental ideas behind the equivalence principle.Comment: LaTeX, 24 pages. To be published in Classical and Quantum Gravit