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In this chapter we focus on \(n\)-DBI gravity and uncover its theoretical aspects. To begin with, in Sect. 3.1 we show that solutions of \(n\)-DBI gravity include any solutions of general relativity with a specific property of the curvature and effects of the space-time foliation appear in the solutions which cannot be removed by allowed coordinate transformations. Next, in Sect. 3.2 we reveal the existence of a scalar graviton originated with a preferred space-time foliation based on Dirac’s theory of constrained systems and investigate its possible pathological behaviors. As it turns out, the scalar mode does not propagate and there is no evidence of the pathology related to the scalar graviton such as vanishing lapse, instabilities and strong self-coupling at low energy scales.
Keywords\(n\)-DBI gravity Dirac’s theory of constrained systems Scalar graviton
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