Tackling nonlinearities with the effective field theory of dark energy and modified gravity
Abstract
We present the extension of the effective field theory framework to the mildly nonlinear scales. The effective field theory approach has been successfully applied to the late time cosmic acceleration phenomenon and it has been shown to be a powerful method to obtain predictions about cosmological observables on linear scales. However, mildly nonlinear scales need to be consistently considered when testing gravity theories because a large part of the data comes from those scales. Thus, nonlinear corrections to predictions on observables coming from the linear analysis can help in discriminating among different gravity theories. We proceed firstly by identifying the necessary operators which need to be included in the effective field theory Lagrangian in order to go beyond the linear order in perturbations and then we construct the corresponding nonlinear action. Moreover, we present the complete recipe to map any single field dark energy and modified gravity models into the nonlinear effective field theory framework by considering a general action in the ArnowittDeserMisner formalism. In order to illustrate this recipe we proceed to map the beyondHorndeski theory and lowenergy Hořava gravity into the effective field theory formalism. As a final step we derived the 4th order action in term of the curvature perturbation. This allowed us to identify the nonlinear contributions coming from the linear order perturbations which at the next order act like source terms. Moreover, we confirm that the stability requirements, ensuring the positivity of the kinetic term and the speed of propagation for scalar mode, are automatically satisfied once the viability of the theory is demanded at linear level. The approach we present here will allow to construct, in a model independent way, all the relevant predictions on observables at mildly nonlinear scales.
 Publication:

Journal of Cosmology and Astroparticle Physics
 Pub Date:
 December 2017
 DOI:
 10.1088/14757516/2017/12/014
 arXiv:
 arXiv:1706.02719
 Bibcode:
 2017JCAP...12..014F
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 19 pages. Sec IV and Appendix B added. Matches JCAP version