Effective field theory of modified gravity with two scalar fields: Dark energy and dark matter

László Á Gergely*, Shinji Tsujikawa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

57 Citations (Scopus)


We present a framework for discussing the cosmology of dark energy and dark matter based on two scalar degrees of freedom. An effective field theory of cosmological perturbations is employed. A unitary gauge choice renders the dark energy field into the gravitational sector, for which we adopt a generic Lagrangian depending on three-dimensional geometrical scalar quantities arising in the Arnowitt-Deser-Misner decomposition. We add to this dark energy-associated gravitational sector a scalar field φ and its kinetic energy X as dark matter variables. Compared to the single-field case, we find that there are additional conditions to obey in order to keep the equations of motion for linear cosmological perturbations at second order. For such a second-order multifield theory, we derive conditions under which ghosts and Laplacian instabilities of the scalar and tensor perturbations are absent. We apply our general results to models with dark energy emerging in the framework of the Horndeski theory and dark matter described by a k-essence Lagrangian P(φ,X). We derive the effective coupling between such an imperfect-fluid dark matter and the gravitational sector under the quasistatic approximation on subhorizon scales. By considering the purely kinetic Lagrangian P(X) as a particular case, the formalism is verified to reproduce the gravitational coupling of a perfect-fluid dark matter.

Original languageEnglish
Article number064059
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number6
Publication statusPublished - 2014 Mar 25
Externally publishedYes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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