Cosmology in generalized Horndeski theories with second-order equations of motion

Ryotaro Kase; Shinji Tsujikawa

doi:10.1103/PhysRevD.90.044073

paper

Cosmology in generalized Horndeski theories with second-order equations of motion

arXiv:1407.0794 · doi:10.1103/PhysRevD.90.044073

Abstract

We study the cosmology of an extended version of Horndeski theories with second-order equations of motion on the flat Friedmann-Lemaître-Robertson-Walker (FLRW) background. In addition to a dark energy field $χ$ associated with the gravitational sector, we take into account multiple scalar fields $ϕ_{I}$ ( $I = 1, 2 \dots, N - 1$ ) characterized by the Lagrangians $P^{(I)} (X_{I})$ with $X_{I} = \partial_{μ} ϕ_{I} \partial^{μ} ϕ_{I}$ . These additional scalar fields can model the perfect fluids of radiation and non-relativistic matter. We derive propagation speeds of scalar and tensor perturbations as well as conditions for the absence of ghosts. The theories beyond Horndeski induce non-trivial modifications to all the propagation speeds of $N$ scalar fields, but the modifications to those for the matter fields $ϕ_{I}$ are generally suppressed relative to that for the dark energy field $χ$ . We apply our results to the covariantized Galileon with an Einstein-Hilbert term in which partial derivatives of the Minkowski Galileon are replaced by covariant derivatives. Unlike the covariant Galileon with second-order equations of motion in general space-time, the scalar propagation speed square $c_{s 1}^{2}$ associated with the field $χ$ becomes negative during the matter era for late-time tracking solutions, so the two Galileon theories can be clearly distinguished at the level of linear cosmological perturbations.

arXiv comment16 pages, 1 figure

Cosmology in generalized Horndeski theories with second-order equations of motion

Abstract

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