### Abstract

It was previously found that in a certain parameter subspace of scalar-tensor theories emerging from massive gravity, the only stable field configuration created by static spherically symmetric sources was one with cosmological asymptotics. Moreover, these backgrounds were shown to be subluminal everywhere in the space; in contrast to the common belief that these theories are necessarily superluminal in the vicinity of a static source. In this work, we complete that analysis by extending it to cover the whole parameter space of these scalar-tensor theories. We find that the stability argument renders the asymptotically flat backgrounds unrealizable, forcing once again for cosmological asymptotics. In the case of pressure-less sources, these backgrounds are stable. However, they get destabilized in the presence of positive pressure, larger than a critical density. Even on the self-accelerated background, on which the scalar mode decouples from sources, in the region occupied by the source it acquires an elliptic equation of motion. Therefore, we conclude that the only parameter space which is not ruled out, by solar system measurements, is the one considered in Berezhiani et al (2013 arXiv:1302.0549), namely the one for which the scalar and tensor modes can be diagonalized via local transformations. We also reinvestigate the scale at which a perturbation theory breaks down in a general Galileon theory. We show that the Vainshtein mechanism successfully redresses the strong-coupling scale to a small one, just like in the cubic Galileon, despite the cancellations occurring in the special spherically symmetric case. We emphasize that even if these tests were performed at scales at which the perturbation theory broke down, these could not be interpreted as a lower bound for the graviton mass.

Original language | English (US) |
---|---|

Article number | 184003 |

Journal | Classical and Quantum Gravity |

Volume | 30 |

Issue number | 18 |

DOIs | |

State | Published - Sep 21 2013 |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Classical and Quantum Gravity*,

*30*(18), [184003]. https://doi.org/10.1088/0264-9381/30/18/184003

**Mixed Galileons and spherically symmetric solutions.** / Berezhiani, L.; Chkareuli, G.; De Rham, C.; Gabadadze, G.; Tolley, A. J.

Research output: Contribution to journal › Article

*Classical and Quantum Gravity*, vol. 30, no. 18, 184003. https://doi.org/10.1088/0264-9381/30/18/184003

}

TY - JOUR

T1 - Mixed Galileons and spherically symmetric solutions

AU - Berezhiani, L.

AU - Chkareuli, G.

AU - De Rham, C.

AU - Gabadadze, G.

AU - Tolley, A. J.

PY - 2013/9/21

Y1 - 2013/9/21

N2 - It was previously found that in a certain parameter subspace of scalar-tensor theories emerging from massive gravity, the only stable field configuration created by static spherically symmetric sources was one with cosmological asymptotics. Moreover, these backgrounds were shown to be subluminal everywhere in the space; in contrast to the common belief that these theories are necessarily superluminal in the vicinity of a static source. In this work, we complete that analysis by extending it to cover the whole parameter space of these scalar-tensor theories. We find that the stability argument renders the asymptotically flat backgrounds unrealizable, forcing once again for cosmological asymptotics. In the case of pressure-less sources, these backgrounds are stable. However, they get destabilized in the presence of positive pressure, larger than a critical density. Even on the self-accelerated background, on which the scalar mode decouples from sources, in the region occupied by the source it acquires an elliptic equation of motion. Therefore, we conclude that the only parameter space which is not ruled out, by solar system measurements, is the one considered in Berezhiani et al (2013 arXiv:1302.0549), namely the one for which the scalar and tensor modes can be diagonalized via local transformations. We also reinvestigate the scale at which a perturbation theory breaks down in a general Galileon theory. We show that the Vainshtein mechanism successfully redresses the strong-coupling scale to a small one, just like in the cubic Galileon, despite the cancellations occurring in the special spherically symmetric case. We emphasize that even if these tests were performed at scales at which the perturbation theory broke down, these could not be interpreted as a lower bound for the graviton mass.

AB - It was previously found that in a certain parameter subspace of scalar-tensor theories emerging from massive gravity, the only stable field configuration created by static spherically symmetric sources was one with cosmological asymptotics. Moreover, these backgrounds were shown to be subluminal everywhere in the space; in contrast to the common belief that these theories are necessarily superluminal in the vicinity of a static source. In this work, we complete that analysis by extending it to cover the whole parameter space of these scalar-tensor theories. We find that the stability argument renders the asymptotically flat backgrounds unrealizable, forcing once again for cosmological asymptotics. In the case of pressure-less sources, these backgrounds are stable. However, they get destabilized in the presence of positive pressure, larger than a critical density. Even on the self-accelerated background, on which the scalar mode decouples from sources, in the region occupied by the source it acquires an elliptic equation of motion. Therefore, we conclude that the only parameter space which is not ruled out, by solar system measurements, is the one considered in Berezhiani et al (2013 arXiv:1302.0549), namely the one for which the scalar and tensor modes can be diagonalized via local transformations. We also reinvestigate the scale at which a perturbation theory breaks down in a general Galileon theory. We show that the Vainshtein mechanism successfully redresses the strong-coupling scale to a small one, just like in the cubic Galileon, despite the cancellations occurring in the special spherically symmetric case. We emphasize that even if these tests were performed at scales at which the perturbation theory broke down, these could not be interpreted as a lower bound for the graviton mass.

UR - http://www.scopus.com/inward/record.url?scp=84884395290&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884395290&partnerID=8YFLogxK

U2 - 10.1088/0264-9381/30/18/184003

DO - 10.1088/0264-9381/30/18/184003

M3 - Article

VL - 30

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 18

M1 - 184003

ER -