On the scalar graviton in n-DBI gravity

TL;DR

This paper investigates n-DBI gravity, revealing it has an extra scalar graviton degree of freedom due to Lorentz invariance breaking, and finds it does not exhibit typical pathologies associated with such extra modes.

Contribution

It demonstrates the existence of a scalar graviton in n-DBI gravity and analyzes its properties using Dirac's constrained systems and ADM formalism.

Findings

n-DBI gravity has an extra scalar degree of freedom.

The scalar graviton is identified via metric perturbations and canonical analysis.

No evidence of pathologies like instabilities or strong coupling at low energies.

Abstract

n-DBI gravity is a gravitational theory which yields near de Sitter inflation spontaneously at the cost of breaking Lorentz invariance by a preferred choice of foliation. We show that this breakdown endows n-DBI gravity with one extra physical gravitational degree of freedom: a scalar graviton. Its existence is established by Dirac's theory of constrained systems. Firstly, studying scalar perturbations around Minkowski space-time, we show that there exists one scalar degree of freedom and identify it in terms of the metric perturbations. Then, a general analysis is made in the canonical formalism, using ADM variables. It is useful to introduce an auxiliary scalar field, which allows recasting n-DBI gravity in an Einstein-Hilbert form but in a Jordan frame. Identifying the constraints and their classes we confirm the existence of an extra degree of freedom in the full theory, besides the two usual tensorial modes of the graviton. We then argue that, unlike the case of (the original proposal for) Horava-Lifschitz gravity, there is no evidence that the extra degree of freedom originates pathologies, such as vanishing lapse, instabilities and strong self-coupling at low energy scales.