# The phenomenology of beyond Horndeski gravity

## TL;DR

This paper investigates the phenomenology of beyond Horndeski gravity theories, linking the extra function to observable cosmological effects, and constrains these theories using CMB and large scale structure data.

## Contribution

It provides a detailed analysis of how the beyond Horndeski parameter $\alpha_{
m H}$ affects cosmological observables and derives observational constraints on this parameter.

## Key findings

- $\alpha_{
m H}$ influences matter power spectrum damping.
- CMB temperature power spectrum is enhanced at low multipoles.
- Constraints on $\alpha_{
m H}$ are of order 1 from current data.

## Abstract

We study the phenomenology of the beyond Horndeski class of scalar-tensor theories of gravity, which on cosmological scales can be characterised in terms of one extra function of time, $\alpha_{\rm H}$, as well as the usual four Horndeski set of free functions. We show that $\alpha_{\rm H}$ can be directly related to the the damping of the matter power spectrum on both large and small scales. We also find that the temperature power spectrum of the cosmic microwave background (CMB) is enhanced at low multipoles and the lensing potential is decreased, as a function of $\alpha_{\rm H}$. We find constraints on $\alpha_{\rm H}$ of order ${\cal O}(1)$ using measurements of the temperature and polarisation of the CMB, as well as the lensing potential derived from it, combined with large scale structure data. We find that redshift space distortion measurements can play a significant role in constraining these theories. Finally, we comment on the recent constraints from the observation of an electromagnetic counterpart to a gravitational wave signal; we find that these constraints reduce the number of free parameters of the model but do not significantly change the constraints on the remaining parameters.