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Recently Horava proposed a model for gravity which is described by the Einstein action in the infrared, but lacks the Lorentz invariance in the high-energy region where it experiences the anisotropic scaling.
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G. Calcagni, Cosmology of the Lifshitz universe, arXiv:0904.0829
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P. Hořava, Spectral dimension of the Universe in quantum gravity at a Lifshitz point, Phys. Rev. Lett. 102
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P. Hořava, Quantum gravity at a Lifshitz point, Phys. Rev. D 79
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