Stability of the early universe in bigravity theory

Katsuki Aoki, Keiichi Maeda, Ryo Namba

    Research output: Contribution to journalArticle

    17 Citations (Scopus)

    Abstract

    We study the stability of a spherically symmetric perturbation around the flat Friedmann-Lemaître-Robertson-Walker spacetime in the ghost-free bigravity theory, retaining nonlinearities of the helicity-0 mode of the massive graviton. It has been known that, when the graviton mass is smaller than the Hubble parameter, homogeneous and isotropic spacetimes suffer from the Higuchi-type ghost or the gradient instability against the linear perturbation in the bigravity. Hence, the bigravity theory has no healthy massless limit for cosmological solutions at linear level. In this paper we show that the instabilities can be resolved by taking into account nonlinear effects of the scalar graviton mode for an appropriate parameter space of coupling constants. The growth history in the bigravity can be restored to the result in general relativity in the early stage of the Universe, in which the Stückelberg fields are nonlinear and there is neither ghost nor gradient instability. Therefore, the bigravity theory has the healthy massless limit, and cosmology based on it is viable even when the graviton mass is smaller than the Hubble parameter.

    Original languageEnglish
    Article number044054
    JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
    Volume92
    Issue number4
    DOIs
    Publication statusPublished - 2015 Aug 28

    Fingerprint

    gravitons
    ghosts
    universe
    perturbation
    gradients
    retaining
    cosmology
    relativity
    nonlinearity
    histories
    scalars

    ASJC Scopus subject areas

    • Nuclear and High Energy Physics

    Cite this

    Stability of the early universe in bigravity theory. / Aoki, Katsuki; Maeda, Keiichi; Namba, Ryo.

    In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 92, No. 4, 044054, 28.08.2015.

    Research output: Contribution to journalArticle

    @article{0c76efb40c6542faa9b67892809f3acd,
    title = "Stability of the early universe in bigravity theory",
    abstract = "We study the stability of a spherically symmetric perturbation around the flat Friedmann-Lema{\^i}tre-Robertson-Walker spacetime in the ghost-free bigravity theory, retaining nonlinearities of the helicity-0 mode of the massive graviton. It has been known that, when the graviton mass is smaller than the Hubble parameter, homogeneous and isotropic spacetimes suffer from the Higuchi-type ghost or the gradient instability against the linear perturbation in the bigravity. Hence, the bigravity theory has no healthy massless limit for cosmological solutions at linear level. In this paper we show that the instabilities can be resolved by taking into account nonlinear effects of the scalar graviton mode for an appropriate parameter space of coupling constants. The growth history in the bigravity can be restored to the result in general relativity in the early stage of the Universe, in which the St{\"u}ckelberg fields are nonlinear and there is neither ghost nor gradient instability. Therefore, the bigravity theory has the healthy massless limit, and cosmology based on it is viable even when the graviton mass is smaller than the Hubble parameter.",
    author = "Katsuki Aoki and Keiichi Maeda and Ryo Namba",
    year = "2015",
    month = "8",
    day = "28",
    doi = "10.1103/PhysRevD.92.044054",
    language = "English",
    volume = "92",
    journal = "Physical review D: Particles and fields",
    issn = "0556-2821",
    publisher = "American Institute of Physics Publising LLC",
    number = "4",

    }

    TY - JOUR

    T1 - Stability of the early universe in bigravity theory

    AU - Aoki, Katsuki

    AU - Maeda, Keiichi

    AU - Namba, Ryo

    PY - 2015/8/28

    Y1 - 2015/8/28

    N2 - We study the stability of a spherically symmetric perturbation around the flat Friedmann-Lemaître-Robertson-Walker spacetime in the ghost-free bigravity theory, retaining nonlinearities of the helicity-0 mode of the massive graviton. It has been known that, when the graviton mass is smaller than the Hubble parameter, homogeneous and isotropic spacetimes suffer from the Higuchi-type ghost or the gradient instability against the linear perturbation in the bigravity. Hence, the bigravity theory has no healthy massless limit for cosmological solutions at linear level. In this paper we show that the instabilities can be resolved by taking into account nonlinear effects of the scalar graviton mode for an appropriate parameter space of coupling constants. The growth history in the bigravity can be restored to the result in general relativity in the early stage of the Universe, in which the Stückelberg fields are nonlinear and there is neither ghost nor gradient instability. Therefore, the bigravity theory has the healthy massless limit, and cosmology based on it is viable even when the graviton mass is smaller than the Hubble parameter.

    AB - We study the stability of a spherically symmetric perturbation around the flat Friedmann-Lemaître-Robertson-Walker spacetime in the ghost-free bigravity theory, retaining nonlinearities of the helicity-0 mode of the massive graviton. It has been known that, when the graviton mass is smaller than the Hubble parameter, homogeneous and isotropic spacetimes suffer from the Higuchi-type ghost or the gradient instability against the linear perturbation in the bigravity. Hence, the bigravity theory has no healthy massless limit for cosmological solutions at linear level. In this paper we show that the instabilities can be resolved by taking into account nonlinear effects of the scalar graviton mode for an appropriate parameter space of coupling constants. The growth history in the bigravity can be restored to the result in general relativity in the early stage of the Universe, in which the Stückelberg fields are nonlinear and there is neither ghost nor gradient instability. Therefore, the bigravity theory has the healthy massless limit, and cosmology based on it is viable even when the graviton mass is smaller than the Hubble parameter.

    UR - http://www.scopus.com/inward/record.url?scp=84940825779&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84940825779&partnerID=8YFLogxK

    U2 - 10.1103/PhysRevD.92.044054

    DO - 10.1103/PhysRevD.92.044054

    M3 - Article

    AN - SCOPUS:84940825779

    VL - 92

    JO - Physical review D: Particles and fields

    JF - Physical review D: Particles and fields

    SN - 0556-2821

    IS - 4

    M1 - 044054

    ER -