# Cosmological constraints and phenomenology of a beyond-Horndeski model

## TL;DR

This paper investigates a beyond-Horndeski dark energy model, deriving tight observational constraints on its parameters and comparing its fit to cosmological data against the standard Lambda-CDM model.

## Contribution

It provides the first comprehensive observational constraints on the beyond-Horndeski parameter lpha_H and compares the model's fit to current cosmological data with lpha_H=0 and lpha_H.

## Key findings

- Planck CMB data constrains lpha_H to 0^{-6}
- The model suppresses the large-scale ISW effect compared to DM
- The model fits the data slightly better than DM according to  statistics

## Abstract

We study observational constraints on a specific dark energy model in the framework of Gleyzes-Langlois-Piazza-Vernizzi theories, which extends the Galileon ghost condensate (GGC) to the domain of beyond Horndeski theories. In this model, we show that the Planck cosmic microwave background (CMB) data, combined with datasets of baryon acoustic oscillations, supernovae type Ia, and redshift-space distortions, give the tight upper bound $|\alpha_{\rm H}^{(0)}| \le {\cal O}(10^{-6})$ on today's beyond-Horndeski (BH) parameter $\alpha_{\rm H}$. This is mostly attributed to the shift of CMB acoustic peaks induced by the early-time changes of cosmological background and perturbations arising from the dominance of $\alpha_{\rm H}$ in the dark energy density. In comparison to the $\Lambda$-cold-dark-matter ($\Lambda$CDM) model, our BH model suppresses the large-scale integrated-Sachs-Wolfe (ISW) tail of CMB temperature anisotropies due to the existence of cubic Galileons, and it modifies the small-scale CMB power spectrum because of the different background evolution. We find that the BH model considered fits the data better than $\Lambda$CDM according to the $\chi^2$ statistics, yet the deviance information criterion (DIC) slightly favors the latter. Given the fact that our BH model with $\alpha_{\rm H}=0$ (i.e., the GGC model) is favored over $\Lambda$CDM even by the DIC, there are no particular signatures for the departure from Horndeski theories in current observations.