Cosmological perturbations in general modified gravity theories

Shinji Tsujikawa*, Antonio De Felice, Shinji Mukohyama

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We derive the equations of linear cosmological perturbations for the general Lagrangian density f(R, φ,X)/2+Lc, where R is a Ricci scalar, φ is a scalar field, and X = - δμφδμφ/2 is a field kinetic energy. We take into account a nonlinear self-interaction term Lc = ξ(φ)φ(δμφδμφ), which keeps the field equations at second order. Taking into account a scalar-field mass explicitly, the equations of matter density perturbations and gravitational potentials are obtained under a quasi-static approximation on sub-horizon scales. We also derive conditions for the avoidance of ghosts and Laplacian instabilities associated with propagation speeds.

Original languageEnglish
Pages (from-to)188-196
Number of pages9
JournalProgress of Theoretical Physics Supplement
Issue number190
Publication statusPublished - 2011
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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