Novel matter coupling in general relativity via canonical transformation

Katsuki Aoki, Chunshan Lin, Shinji Mukohyama

    Research output: Contribution to journalArticle

    8 Citations (Scopus)

    Abstract

    We study canonical transformations of general relativity (GR) to provide a novel matter coupling to gravity. Although the transformed theory is equivalent to GR in vacuum, the equivalence no longer holds if a matter field minimally couples to the canonically transformed gravitational field. We find that a naive matter coupling to the transformed field leads to the appearance of an extra mode in the phase space, rendering the theory inconsistent. We then find a consistent and novel way of matter coupling: after imposing a gauge fixing condition, a matter field can minimally couple to gravity without generating an unwanted extra mode. As a result, the way matter field couples to the gravitational field determines the preferred time direction and the resultant theory has only two gravitational degrees of freedom. We also discuss the cosmological solution and linear perturbations around it, and confirm that their dynamics indeed differ from those in GR. The novel matter coupling can be used for a new framework of modified gravity theories.

    Original languageEnglish
    Article number044022
    JournalPhysical Review D
    Volume98
    Issue number4
    DOIs
    Publication statusPublished - 2018 Aug 15

    ASJC Scopus subject areas

    • Physics and Astronomy (miscellaneous)

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