# Horndeski dark matter and beyond

## TL;DR

This paper develops a generalized scalar-tensor theory derived from the Gleyzes-Langlois-Piazza-Vernizzi action, showing it can mimic cold dark matter behavior in certain conditions but cannot fully replace dark matter due to couplings with baryons.

## Contribution

It introduces the most general effective theory invariant under specific symmetries, extending Horndeski models, and analyzes its dark matter and gravitational wave properties.

## Key findings

- Scalar mode clusters like cold dark matter in an empty universe.
- Model matches gravitational wave speed constraints from multimessenger observations.
- Couplings to baryons prevent the scalar from behaving exactly as cold dark matter.

## Abstract

Starting from the Gleyzes-Langlois-Piazza-Vernizzi action, we derive the most general effective theory that is invariant under internal shifts and a $\mathbb{Z}_2$ mirror symmetry in the scalar sector. Contrary to what one may think, this model presents a dark matter tracker previous to the dark energy domination. We show that, in an empty universe and to linear order in perturbations, the scalar mode clusters in exactly the same way as standard nonrelativistic cold dark matter. This also holds for the subsector of the theory where the speed of propagation of gravitational waves equals that of light, in agreement with the recent multimessenger observation. However, the inclusion of standard model particles introduces nontrivial couplings of the gravitational scalar mode to baryons, modifying their clustering properties. We argue that no arrangement of the parameters of the model can reduce the extra scalar to precisely behave as cold dark matter.