Third order solutions of the cosmological density perturbations in the Horndeski's most general scalar-tensor theory with the Vainshtein mechanism

TL;DR

This paper derives third order solutions for cosmological density perturbations within the most general scalar-tensor theory, analyzing their properties and implications for power spectra, especially under the Vainshtein mechanism.

Contribution

It provides a comprehensive analysis of third order perturbation solutions in Horndeski theories, highlighting parameter dependencies and effects on power spectra.

Findings

Solutions characterized by 6 parameters for density and velocity fields

1-loop power spectra depend on 4 parameters

Modified gravity effects are more prominent in velocity divergence power spectrum

Abstract

We study the third order solutions of the cosmological density perturbations in the Horndeski's most general scalar-tensor theory under the condition that the Vainshtein mechanism is at work. In this work, we thoroughly investigate the independence property of the functions describing the nonlinear mode-couplings, which is also useful for models within the general relativity. Then, we find that the solutions of the density contrast and the velocity divergence up to the third order ones are characterized by 6 parameters. Furthermore, the 1-loop order power spectra obtained with the third order solutions are described by 4 parameters. We exemplify the behavior of the 1-loop order power spectra assuming the kinetic gravity braiding model, which demonstrates that the effect of the modified gravity appears more significantly in the power spectrum of the velocity divergence than the density contrast.