TY - JOUR
T1 - Effective field theory of modified gravity with two scalar fields
T2 - Dark energy and dark matter
AU - Gergely, László Á
AU - Tsujikawa, Shinji
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2014/3/25
Y1 - 2014/3/25
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84898737086&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84898737086&partnerID=8YFLogxK
U2 - 10.1103/PhysRevD.89.064059
DO - 10.1103/PhysRevD.89.064059
M3 - Article
AN - SCOPUS:84898737086
VL - 89
JO - Physical Review D - Particles, Fields, Gravitation and Cosmology
JF - Physical Review D - Particles, Fields, Gravitation and Cosmology
SN - 1550-7998
IS - 6
M1 - 064059
ER -