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n-DBI gravity explicitly breaks Lorentz invariance by the introduction of a unit time-like vector field, thereby giving rise to an extra (scalar) degree of freedom.
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B. Z. Foster, T. Jacobson, “Post-Newtonian parameters and constraints on Einstein-aether theory,” Phys. Rev. D 73
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D. Langlois, “Lectures on inflation and cosmological perturbations,” Lect. Notes Phys. 800
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2010
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C. Herdeiro, S. Hirano, Y. Sato, “n-DBI gravity,” Phys. Rev. D 84
2011
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2011
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2012
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A. Riotto, “Inflation and the theory of cosmological perturbations,” hep-ph/0210162
Cited in the paper.