Observational signatures of the theories beyond Horndeski

Antonio De Felice; Kazuya Koyama; Shinji Tsujikawa

doi:10.1088/1475-7516/2015/05/058

paper

Observational signatures of the theories beyond Horndeski

arXiv:1503.06539 · doi:10.1088/1475-7516/2015/05/058

Abstract

In the approach of the effective field theory of modified gravity, we derive the equations of motion for linear perturbations in the presence of a barotropic perfect fluid on the flat isotropic cosmological background. In a simple version of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories, which is the minimum extension of Horndeski theories, we show that a slight deviation of the tensor propagation speed squared $c_{t}^{2}$ from 1 generally leads to the large modification to the propagation speed squared $c_{s}^{2}$ of a scalar degree of freedom $ϕ$ . This problem persists whenever the kinetic energy $ρ_{X}$ of the field $ϕ$ is much smaller than the background energy density $ρ_{m}$ , which is the case for most of dark energy models in the asymptotic past. Since the scaling solution characterized by the constant ratio $ρ_{X} / ρ_{m}$ is one way out for avoiding such a problem, we study the evolution of perturbations for a scaling dark energy model in the framework of GLPV theories in the Jordan frame. Provided the oscillating mode of scalar perturbations is fine-tuned so that it is initially suppressed, the anisotropic parameter $η = - Φ/Ψ$ between the two gravitational potentials $Ψ$ and $Φ$ significantly deviates from 1 for $c_{t}^{2}$ away from 1. For other general initial conditions, the deviation of $c_{t}^{2}$ from 1 gives rise to the large oscillation of $Ψ$ with the frequency related to $c_{s}^{2}$ . In both cases, the model can leave distinct imprints for the observations of CMB and weak lensing.

arXiv comment20 pages, 4 figures, published in JCAP

Observational signatures of the theories beyond Horndeski

Abstract

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