# Nonlinear properties of vielbein massive gravity

@article{GrootNibbelink2007NonlinearPO, title={Nonlinear properties of vielbein massive gravity}, author={S. Groot Nibbelink and Marco Peloso and M G Sexton}, journal={The European Physical Journal C}, year={2007}, volume={51}, pages={741-752} }

We propose a nonlinear extension of the Fierz–Pauli mass for the graviton through a functional of the vielbein and an external Minkowski background. The functional generalizes the notion of the measure, since it reduces to a cosmological constant if the external background is formally sent to zero. Such a term and the explicit external background emerge dynamically from a bi-gravity theory, having both a massless and a massive graviton in its spectrum, in a specific limit in which the massless…

## 48 Citations

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## References

SHOWING 1-10 OF 59 REFERENCES

### Chiral gravity as a covariant formulation of massive gravity

- Physics
- 2005

We present a covariant nonlinear completion of the Fierz–Pauli (FP) mass term for the graviton. The starting observation is that the FP mass is immediately obtained by expanding the cosmological…

### Phases of massive gravity

- Physics, Geology
- 2004

We systematically study the most general Lorentz-violating graviton mass invariant under three-dimensional Eucledian group. We find that at general values of mass parameters the massive graviton has…

### Graviton Mass or Cosmological Constant

- Physics
- 2005

To describe a massive graviton in 4D Minkowski space-time one introduces a quadratic term in the Lagrangian. This term, however, can lead to a readjustment or instability of the background instead of…

### Nonlinear bigravity and cosmic acceleration

- Physics
- 2002

We explore the cosmological solutions of classes of nonlinear bigravity theories. These theories are defined by effective four-dimensional Lagrangians describing the coupled dynamics of two metric…

### Ghost condensation and a consistent infrared modification of gravity

- Physics
- 2003

We propose a theoretically consistent modification of gravity in the infrared, which is compatible with all current experimental observations. This is an analog of the Higgs mechanism in general…

### Nonperturbative Continuity in Graviton Mass versus Perturbative Discontinuity

- Physics
- 2002

We address the question whether a graviton could have a small nonzero mass. The issue is subtle for two reasons: there is a discontinuity in the mass in the lowest tree-level approximation, and,…

### Modified gravity via spontaneous symmetry breaking

- Physics
- 2004

We construct effective field theories in which gravity is modified via spontaneous breaking of local Lorentz invariance. This is a gravitational analogue of the Higgs mechanism. These theories…

### Classical and Quantum Consistency of the DGP Model

- Physics
- 2004

We study the Dvali-Gabadadze-Porrati model by the method of the boundary effective action. The truncation of this action to the bending mode π consistently describes physics in a wide range of…

### Ghosts in massive gravity

- Physics
- 2005

In the context of Lorentz-invariant massive gravity we show that classical solutions around heavy sources are plagued by ghost instabilities. The ghost shows up in the effective field theory at huge…