# Fab Four Effective Field Theory Treatment

## TL;DR

This paper investigates the John interaction in Fab Four Horndeski models within the effective field theory framework, revealing new curvature terms and additional gravitational degrees of freedom, some of which are ghosts or decay.

## Contribution

It demonstrates how John interaction induces quadratic curvature terms and new gravitational degrees of freedom in the effective field theory context, highlighting potential issues like ghosts.

## Key findings

- John interaction adds quadratic curvature terms
- New scalar and spin-2 degrees of freedom are generated
- Some degrees of freedom are ghosts or have decay widths

## Abstract

The article addresses the John interaction from Fab Four class of Horndeski models from the effective field theory point of view. Models with this interaction are heavily constrained by gravitational wave speed observations, so it is important to understand, if these constraints hold in the effective field theory framework. We show that John interaction induces new terms quadratic in curvature at the level of the effective (classical) action. These new terms generate additional low energy scalar and spin-2 gravitational degrees of freedom. Some of them have a non-vanishing decay width and some are ghosts. Discussion of these features is given