Galileon and generalized Galileon with projective invariance in a metric-affine formalism

Katsuki Aoki, Keigo Shimada

    Research output: Contribution to journalArticle

    6 Citations (Scopus)

    Abstract

    We study scalar-tensor theories respecting the projective invariance in the metric-affine formalism. The metric-affine formalism is a formulation of gravitational theories such that the metric and the connection are independent variables in the first place. In this formalism, the Einstein-Hilbert action has an additional invariance, called the projective invariance, under a shift of the connection. Respecting this invariance for the construction of the scalar-tensor theories, we find that the Galileon terms in curved spacetime are uniquely specified at least up to quartic order which does not coincide with either the covariant Galileon or the covariantized Galileon. We also find an action in the metric-affine formalism which is equivalent to class N2-I/Ia of the quadratic degenerated higher order scalar-tensor (DHOST) theory. The structure of DHOST would become clear in the metric-affine formalism since the equivalent action is just linear in the generalized Galileon terms and non-minimal couplings to the Ricci scalar and the Einstein tensor with independent coefficients. The fine-tuned structure of DHOST is obtained by integrating out the connection. In these theories, nonminimal couplings between fermionic fields and the scalar field may be predicted. We discuss possible extensions which could involve theories beyond DHOST.

    Original languageEnglish
    Article number044038
    JournalPhysical Review D
    Volume98
    Issue number4
    DOIs
    Publication statusPublished - 2018 Aug 15

    Fingerprint

    invariance
    scalars
    formalism
    tensors
    fine structure
    formulations
    shift
    coefficients

    ASJC Scopus subject areas

    • Physics and Astronomy (miscellaneous)

    Cite this

    Galileon and generalized Galileon with projective invariance in a metric-affine formalism. / Aoki, Katsuki; Shimada, Keigo.

    In: Physical Review D, Vol. 98, No. 4, 044038, 15.08.2018.

    Research output: Contribution to journalArticle

    @article{43b69ebe15f74c228365a4267dfad4b4,
    title = "Galileon and generalized Galileon with projective invariance in a metric-affine formalism",
    abstract = "We study scalar-tensor theories respecting the projective invariance in the metric-affine formalism. The metric-affine formalism is a formulation of gravitational theories such that the metric and the connection are independent variables in the first place. In this formalism, the Einstein-Hilbert action has an additional invariance, called the projective invariance, under a shift of the connection. Respecting this invariance for the construction of the scalar-tensor theories, we find that the Galileon terms in curved spacetime are uniquely specified at least up to quartic order which does not coincide with either the covariant Galileon or the covariantized Galileon. We also find an action in the metric-affine formalism which is equivalent to class N2-I/Ia of the quadratic degenerated higher order scalar-tensor (DHOST) theory. The structure of DHOST would become clear in the metric-affine formalism since the equivalent action is just linear in the generalized Galileon terms and non-minimal couplings to the Ricci scalar and the Einstein tensor with independent coefficients. The fine-tuned structure of DHOST is obtained by integrating out the connection. In these theories, nonminimal couplings between fermionic fields and the scalar field may be predicted. We discuss possible extensions which could involve theories beyond DHOST.",
    author = "Katsuki Aoki and Keigo Shimada",
    year = "2018",
    month = "8",
    day = "15",
    doi = "10.1103/PhysRevD.98.044038",
    language = "English",
    volume = "98",
    journal = "Physical Review D",
    issn = "2470-0010",
    publisher = "American Physical Society",
    number = "4",

    }

    TY - JOUR

    T1 - Galileon and generalized Galileon with projective invariance in a metric-affine formalism

    AU - Aoki, Katsuki

    AU - Shimada, Keigo

    PY - 2018/8/15

    Y1 - 2018/8/15

    N2 - We study scalar-tensor theories respecting the projective invariance in the metric-affine formalism. The metric-affine formalism is a formulation of gravitational theories such that the metric and the connection are independent variables in the first place. In this formalism, the Einstein-Hilbert action has an additional invariance, called the projective invariance, under a shift of the connection. Respecting this invariance for the construction of the scalar-tensor theories, we find that the Galileon terms in curved spacetime are uniquely specified at least up to quartic order which does not coincide with either the covariant Galileon or the covariantized Galileon. We also find an action in the metric-affine formalism which is equivalent to class N2-I/Ia of the quadratic degenerated higher order scalar-tensor (DHOST) theory. The structure of DHOST would become clear in the metric-affine formalism since the equivalent action is just linear in the generalized Galileon terms and non-minimal couplings to the Ricci scalar and the Einstein tensor with independent coefficients. The fine-tuned structure of DHOST is obtained by integrating out the connection. In these theories, nonminimal couplings between fermionic fields and the scalar field may be predicted. We discuss possible extensions which could involve theories beyond DHOST.

    AB - We study scalar-tensor theories respecting the projective invariance in the metric-affine formalism. The metric-affine formalism is a formulation of gravitational theories such that the metric and the connection are independent variables in the first place. In this formalism, the Einstein-Hilbert action has an additional invariance, called the projective invariance, under a shift of the connection. Respecting this invariance for the construction of the scalar-tensor theories, we find that the Galileon terms in curved spacetime are uniquely specified at least up to quartic order which does not coincide with either the covariant Galileon or the covariantized Galileon. We also find an action in the metric-affine formalism which is equivalent to class N2-I/Ia of the quadratic degenerated higher order scalar-tensor (DHOST) theory. The structure of DHOST would become clear in the metric-affine formalism since the equivalent action is just linear in the generalized Galileon terms and non-minimal couplings to the Ricci scalar and the Einstein tensor with independent coefficients. The fine-tuned structure of DHOST is obtained by integrating out the connection. In these theories, nonminimal couplings between fermionic fields and the scalar field may be predicted. We discuss possible extensions which could involve theories beyond DHOST.

    UR - http://www.scopus.com/inward/record.url?scp=85052622389&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=85052622389&partnerID=8YFLogxK

    U2 - 10.1103/PhysRevD.98.044038

    DO - 10.1103/PhysRevD.98.044038

    M3 - Article

    AN - SCOPUS:85052622389

    VL - 98

    JO - Physical Review D

    JF - Physical Review D

    SN - 2470-0010

    IS - 4

    M1 - 044038

    ER -