# Cosmology of bigravity with doubly coupled matter

## Abstract

We study cosmology in the bigravity formulation of the dRGT model where matter couples to both metrics. At linear order in perturbation theory two mass scales emerge: an hard one from the dRGT potential, and an environmental dependent one from the coupling of bigravity with matter. At early time, the dynamics is dictated by the second mass scale which is of order of the Hubble scale. The set of gauge invariant perturbations that couples to matter follow closely the same behaviour as in GR. The remaining perturbations show no issue in the scalar sector, while problems arise in the tensor and vector sectors. During radiation domination, a tensor mode grows power-like at super-horizon scales. More dangerously, the only propagating vector mode features an exponential instability on sub-horizon scales. We discuss the consequences of such instabilities and speculate on possible ways to deal with them.

- Authors:

- INFN, Sezione di Ferrara, Via Saragat 1, 44122 Ferrara (Italy)
- Institute of Cosmology and Gravitation, University of Portsmouth, Burnaby Road, PO1 3FX, Portsmouth (United Kingdom)
- Dipartimento di Fisica, Università di L’Aquila, Via Vetoio, 67010 L’Aquila (Italy)
- (Italy)
- Department of Physics, Swansea University, Singleton Park, SA2 8PP, Swansea (United Kingdom)

- Publication Date:

- Sponsoring Org.:
- SCOAP3, CERN, Geneva (Switzerland)

- OSTI Identifier:
- 22454539

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; Journal Issue: 04; Other Information: PUBLISHER-ID: JCAP04(2015)026; OAI: oai:repo.scoap3.org:9954; Article funded by SCOAP3. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 License. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COSMOLOGY; GAUGE INVARIANCE; GRAVITATION; METRICS; PERTURBATION THEORY; SCALARS; VECTORS

### Citation Formats

```
Comelli, D., Crisostomi, M., Koyama, K., Pilo, L., INFN, Laboratori Nazionali del Gran Sasso, Via G. Acitelli 22, 67100 Assergi, and Tasinato, G..
```*Cosmology of bigravity with doubly coupled matter*. United States: N. p., 2015.
Web. doi:10.1088/1475-7516/2015/04/026.

```
Comelli, D., Crisostomi, M., Koyama, K., Pilo, L., INFN, Laboratori Nazionali del Gran Sasso, Via G. Acitelli 22, 67100 Assergi, & Tasinato, G..
```*Cosmology of bigravity with doubly coupled matter*. United States. doi:10.1088/1475-7516/2015/04/026.

```
Comelli, D., Crisostomi, M., Koyama, K., Pilo, L., INFN, Laboratori Nazionali del Gran Sasso, Via G. Acitelli 22, 67100 Assergi, and Tasinato, G.. Mon .
"Cosmology of bigravity with doubly coupled matter". United States.
doi:10.1088/1475-7516/2015/04/026.
```

```
@article{osti_22454539,
```

title = {Cosmology of bigravity with doubly coupled matter},

author = {Comelli, D. and Crisostomi, M. and Koyama, K. and Pilo, L. and INFN, Laboratori Nazionali del Gran Sasso, Via G. Acitelli 22, 67100 Assergi and Tasinato, G.},

abstractNote = {We study cosmology in the bigravity formulation of the dRGT model where matter couples to both metrics. At linear order in perturbation theory two mass scales emerge: an hard one from the dRGT potential, and an environmental dependent one from the coupling of bigravity with matter. At early time, the dynamics is dictated by the second mass scale which is of order of the Hubble scale. The set of gauge invariant perturbations that couples to matter follow closely the same behaviour as in GR. The remaining perturbations show no issue in the scalar sector, while problems arise in the tensor and vector sectors. During radiation domination, a tensor mode grows power-like at super-horizon scales. More dangerously, the only propagating vector mode features an exponential instability on sub-horizon scales. We discuss the consequences of such instabilities and speculate on possible ways to deal with them.},

doi = {10.1088/1475-7516/2015/04/026},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 04,

volume = 2015,

place = {United States},

year = {Mon Apr 20 00:00:00 EDT 2015},

month = {Mon Apr 20 00:00:00 EDT 2015}

}