# Screening and degenerate kinetic self-acceleration from the nonlinear freedom of reconstructed Horndeski theories

## TL;DR

This paper explores how nonlinear freedoms in reconstructed Horndeski theories can produce screening mechanisms and degenerate models that mimic standard cosmology, linking linear constraints with nonlinear and astrophysical observations.

## Contribution

It introduces a method to incorporate nonlinear correction terms into Horndeski theories, enabling screening effects and degenerate models, and extends reconstruction to higher-order effective field theories.

## Key findings

- Nonlinear correction terms can produce screening mechanisms like chameleon, k-mouflage, and Vainshtein.
- Existence of Horndeski models degenerate with standard cosmology at the perturbation level.
- Extended reconstruction to higher-order effective field theory with two free functions per order.

## Abstract

We have previously presented a reconstruction of Horndeski scalar-tensor theories from linear cosmological observables. It includes free nonlinear terms which can be added onto the reconstructed covariant theory without affecting the background and linear dynamics. After discussing the uniqueness of these correction terms, we apply this nonlinear freedom to a range of different applications. First we demonstrate how the correction terms can be configured to endow the reconstructed models with screening mechanisms such as the chameleon, k-mouflage and Vainshtein effects. A further implication is the existence of classes of Horndeski models that are degenerate with standard cosmology to an arbitrary level in the cosmological perturbations. Particularly interesting examples are kinetically self-accelerating models that mimic the dynamics of the cosmological constant to an arbitrary degree in perturbations. Finally, we develop the reconstruction method further to the level of higher-order effective field theory, which under the restriction to a luminal propagation speed of gravitational waves introduces two new free functions per order. These functions determine the corresponding correction terms in the linearly reconstructed action at the same order. Our results enable the connection of linear cosmological constraints on generalised modifications of gravity and dark energy with the nonlinear regime and astrophysical probes for a more global interpretation of the wealth of forthcoming cosmological survey data.