# Cosmological perturbations in massive gravity and the Higuchi bound

## Abstract

In de Sitter spacetime there exists an absolute minimum for the mass of a spin-2 field set by the Higuchi bound m{sup 2} ≥ 2H{sup 2}. We generalize this bound to arbitrary spatially flat FRW geometries in the context of the recently proposed ghost-free models of Massive Gravity with an FRW reference metric, by performing a Hamiltonian analysis for cosmological perturbations. We find that the bound generically indicates that spatially flat FRW solutions in FRW massive gravity, which exhibit a Vainshtein mechanism in the background as required by consistency with observations, imply that the helicity zero mode is a ghost. In contradistinction to previous works, the tension between the Higuchi bound and the Vainshtein mechanism is equally strong regardless of the equation of state for matter.

- Authors:

- Department of Physics, Case Western Reserve University, 10900 Euclid Ave, Cleveland, OH 44106 (United States)

- Publication Date:

- OSTI Identifier:
- 22279820

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Cosmology and Astroparticle Physics

- Additional Journal Information:
- Journal Volume: 2012; Journal Issue: 11; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1475-7516

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COSMOLOGICAL MODELS; COSMOLOGY; DISTURBANCES; EQUATIONS OF STATE; GEOMETRY; GRAVITATION; HAMILTONIANS; HELICITY; MATHEMATICAL SOLUTIONS; METRICS; PERTURBATION THEORY; REST MASS; SPIN

### Citation Formats

```
Fasiello, Matteo, and Tolley, Andrew J., E-mail: matte@case.edu, E-mail: andrew.j.tolley@case.edu.
```*Cosmological perturbations in massive gravity and the Higuchi bound*. United States: N. p., 2012.
Web. doi:10.1088/1475-7516/2012/11/035.

```
Fasiello, Matteo, & Tolley, Andrew J., E-mail: matte@case.edu, E-mail: andrew.j.tolley@case.edu.
```*Cosmological perturbations in massive gravity and the Higuchi bound*. United States. doi:10.1088/1475-7516/2012/11/035.

```
Fasiello, Matteo, and Tolley, Andrew J., E-mail: matte@case.edu, E-mail: andrew.j.tolley@case.edu. Thu .
"Cosmological perturbations in massive gravity and the Higuchi bound". United States. doi:10.1088/1475-7516/2012/11/035.
```

```
@article{osti_22279820,
```

title = {Cosmological perturbations in massive gravity and the Higuchi bound},

author = {Fasiello, Matteo and Tolley, Andrew J., E-mail: matte@case.edu, E-mail: andrew.j.tolley@case.edu},

abstractNote = {In de Sitter spacetime there exists an absolute minimum for the mass of a spin-2 field set by the Higuchi bound m{sup 2} ≥ 2H{sup 2}. We generalize this bound to arbitrary spatially flat FRW geometries in the context of the recently proposed ghost-free models of Massive Gravity with an FRW reference metric, by performing a Hamiltonian analysis for cosmological perturbations. We find that the bound generically indicates that spatially flat FRW solutions in FRW massive gravity, which exhibit a Vainshtein mechanism in the background as required by consistency with observations, imply that the helicity zero mode is a ghost. In contradistinction to previous works, the tension between the Higuchi bound and the Vainshtein mechanism is equally strong regardless of the equation of state for matter.},

doi = {10.1088/1475-7516/2012/11/035},

journal = {Journal of Cosmology and Astroparticle Physics},

issn = {1475-7516},

number = 11,

volume = 2012,

place = {United States},

year = {2012},

month = {11}

}