# Cosmology with subdominant Horndeski scalar field

## TL;DR

This paper investigates the evolution of a subdominant scalar field in Horndeski gravity, analyzing constraints from gravitational wave observations and exploring models with scalarization phenomena, highlighting the need for fine-tuning.

## Contribution

It provides a comprehensive analysis of subdominant scalar fields in Horndeski gravity, including constraints from GW170817 and examples of scalarization models with broken shift-symmetry.

## Key findings

- GW170817 constrains scalar-Gauss-Bonnet coupling mildly
- Scalarization models require fine-tuning to keep scalar dormant
- Subdominant scalar fields can evolve without dominating cosmic dynamics

## Abstract

We study the cosmological evolution of a scalar field in Horndeski gravity, assuming that the scalar field is subdominant with respect to the cosmic fluid. We first analyse the most general shift-symmetric action that respects local Lorentz symmetry. We show that the bound on the speed of gravitational waves set by GW170817+GRB170817A imposes a constraint only on the linear coupling between the scalar and the Gauss-Bonnet invariant and this constraint is rather mild. Then, we consider some interesting examples of theories that break shift-symmetry, such as the Damour-Esposito-Far\`ese model of spontaneous scalarization and a theory with a quadratic coupling to the Gauss-Bonnet invariant that can lead to black hole scalarization. In both cases, tuning of cosmological initial conditions is necessary to keep the scalar field dormant during cosmic evolution.