Price for environmental neutrino-superluminality

We ask whether the recent OPERA results on neutrino superluminality could be an environmental effect characteristic of the local neighborhood of our planet, without the need of violation of the Poincaré-invariance at a fundamental level. We show, that model-indepenently, such a possibility implies the existence of new gravitational degrees of freedom. Namely, this explanation requires the existence of a new spin-2 field of a planetary Compton wave-length that is coupled to neutrinos and the rest of the matter asymmetrically, both in the magnitude and in the sign. Sourced by the earth this field creates an effective metric on which neutrinos propagate superluminally, whereas other species are much less sensitive to the background. Such a setup, at an effective field theory level, passes all immediate phenomenological tests, but at the expense of sacrificing calculability for some of the phenomena that are under perturbative control in ordinary gravity. The natural prediction is an inevitable appearance of a testable long-range gravity- type fifth force. Despite phenomenological viability, the sign asymmetry of the coupling we identify as the main potential obstacle for a consistent UV-completion. We also discuss the possible identification of this field with a Kaluza-Klein state of an extra dimension in which neutrino can propagate.