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

Understand

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.