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We study how quantum fluctuations of the metric in covariant Horava-Lifshitzgravity influence the propagation of classical fields (complex scalar andphoton). The effective Lorentz-symmetry violation induced by the breaking of4-dimensional diffeomorphism is then evaluated, by comparing the dresseddispersion relations for both external fields. The constraint of vanishing3-dimensional Ricci scalar is imposed in the path integral, which thereforeexplicitly depends on two propagating gravitational degrees of freedom only.Because the matter fields are classical, the present model contains onlylogarithmic divergences. Furthermore, it imposes the characteristicHorava-Lifshitz scale to be smaller than $10^{10}$ GeV, if one wishes not toviolate the current bounds on Lorentz symmetry violation.

Effective matter dispersion relation in quantum covariant Horava-Lifshitz gravity